1
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Casson CL, John SA, Ferrall-Fairbanks MC. Mathematical modeling of cardio-oncology: Modeling the systemic effects of cancer therapeutics on the cardiovascular system. Semin Cancer Biol 2023; 97:30-41. [PMID: 37979714 DOI: 10.1016/j.semcancer.2023.11.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2022] [Revised: 08/25/2023] [Accepted: 11/12/2023] [Indexed: 11/20/2023]
Abstract
Cardiotoxicity is a common side-effect of many cancer therapeutics; however, to-date there has been very little push to understand the mechanisms underlying this group of pathologies. This has led to the emergence of cardio-oncology, a field of medicine focused on understanding the effects of cancer and its treatment on the human heart. Here, we describe how mechanistic modeling approaches have been applied to study open questions in the cardiovascular system and how these approaches are being increasingly applied to advance knowledge of the underlying effects of cancer treatments on the human heart. A variety of mechanistic, mathematical modeling techniques have been applied to explore the link between common cancer treatments, such as chemotherapy, radiation, targeted therapy, and immunotherapy, and cardiotoxicity, nevertheless there is limited coverage in the different types of cardiac dysfunction that may be associated with these treatments. Moreover, cardiac modeling has a rich heritage of mathematical modeling and is well suited for the further development of novel approaches for understanding the cardiotoxicities associated with cancer therapeutics. There are many opportunities to combine mechanistic, bottom-up approaches with data-driven, top-down approaches to improve personalized, precision oncology to better understand, and ultimately mitigate, cardiac dysfunction in cancer patients.
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Affiliation(s)
- Camara L Casson
- J. Crayton Pruitt Family Department of Biomedical Engineering, University of Florida, Gainesville, FL 32611, USA
| | - Sofia A John
- Department of Statistics, University of Florida, Gainesville, FL 32611, USA
| | - Meghan C Ferrall-Fairbanks
- J. Crayton Pruitt Family Department of Biomedical Engineering, University of Florida, Gainesville, FL 32611, USA; University of Florida Health Cancer Center, University of Florida, Gainesville, FL 32611, USA.
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2
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Jin Q, Greenstein JL, Winslow RL. Estimating the probability of early afterdepolarizations and predicting arrhythmic risk associated with long QT syndrome type 1 mutations. Biophys J 2023; 122:4042-4056. [PMID: 37705243 PMCID: PMC10598291 DOI: 10.1016/j.bpj.2023.09.001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2023] [Revised: 08/29/2023] [Accepted: 09/08/2023] [Indexed: 09/15/2023] Open
Abstract
Early afterdepolarizations (EADs) are action potential (AP) repolarization abnormalities that can trigger lethal arrhythmias. Simulations using biophysically detailed cardiac myocyte models can reveal how model parameters influence the probability of these cellular arrhythmias; however, such analyses can pose a huge computational burden. We have previously developed a highly simplified approach in which logistic regression models (LRMs) map parameters of complex cell models to the probability of ectopic beats. Here, we extend this approach to predict the probability of EADs (P(EAD)) as a mechanistic metric of arrhythmic risk. We use the LRM to investigate how changes in parameters of the slow-activating delayed rectifier current (IKs) affect P(EAD) for 17 different long QT syndrome type 1 (LQTS1) mutations. In this LQTS1 clinical arrhythmic risk prediction task, we compared P(EAD) for these 17 mutations with two other recently published model-based arrhythmia risk metrics (AP morphology metric across populations of myocyte models and transmural repolarization prolongation based on a one-dimensional [1D] tissue-level model). These model-based risk metrics yield similar prediction performance; however, each fails to stratify clinical risk for a significant number of the 17 studied LQTS1 mutations. Nevertheless, an interpretable ensemble model using multivariate linear regression built by combining all of these model-based risk metrics successfully predicts the clinical risk of 17 mutations. These results illustrate the potential of computational approaches in arrhythmia risk prediction.
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Affiliation(s)
- Qingchu Jin
- Department of Biomedical Engineering and Institute for Computational Medicine, Johns Hopkins University, Baltimore, Maryland
| | - Joseph L Greenstein
- Department of Biomedical Engineering and Institute for Computational Medicine, Johns Hopkins University, Baltimore, Maryland
| | - Raimond L Winslow
- Department of Biomedical Engineering and Institute for Computational Medicine, Johns Hopkins University, Baltimore, Maryland.
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3
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Alvarez JAE, Jafri MS, Ullah A. Local Control Model of a Human Ventricular Myocyte: An Exploration of Frequency-Dependent Changes and Calcium Sparks. Biomolecules 2023; 13:1259. [PMID: 37627324 PMCID: PMC10452762 DOI: 10.3390/biom13081259] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2023] [Revised: 08/07/2023] [Accepted: 08/15/2023] [Indexed: 08/27/2023] Open
Abstract
Calcium (Ca2+) sparks are the elementary events of excitation-contraction coupling, yet they are not explicitly represented in human ventricular myocyte models. A stochastic ventricular cardiomyocyte human model that adapts to intracellular Ca2+ ([Ca2+]i) dynamics, spark regulation, and frequency-dependent changes in the form of locally controlled Ca2+ release was developed. The 20,000 CRUs in this model are composed of 9 individual LCCs and 49 RyRs that function as couplons. The simulated action potential duration at 1 Hz steady-state pacing is ~0.280 s similar to human ventricular cell recordings. Rate-dependence experiments reveal that APD shortening mechanisms are largely contributed by the L-type calcium channel inactivation, RyR open fraction, and [Ca2+]myo concentrations. The dynamic slow-rapid-slow pacing protocol shows that RyR open probability during high pacing frequency (2.5 Hz) switches to an adapted "nonconducting" form of Ca2+-dependent transition state. The predicted force was also observed to be increased in high pacing, but the SR Ca2+ fractional release was lower due to the smaller difference between diastolic and systolic [Ca2+]SR. Restitution analysis through the S1S2 protocol and increased LCC Ca2+-dependent activation rate show that the duration of LCC opening helps modulate its effects on the APD restitution at different diastolic intervals. Ultimately, a longer duration of calcium sparks was observed in relation to the SR Ca2+ loading at high pacing rates. Overall, this study demonstrates the spontaneous Ca2+ release events and ion channel responses throughout various stimuli.
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Affiliation(s)
| | - M. Saleet Jafri
- School of Systems Biology, George Mason University, Fairfax, VA 22030, USA;
- Center for Biomedical Engineering and Technology, University of Maryland School of Medicine, Baltimore, MD 20201, USA
| | - Aman Ullah
- School of Systems Biology, George Mason University, Fairfax, VA 22030, USA;
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4
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Grandi E, Navedo MF, Saucerman JJ, Bers DM, Chiamvimonvat N, Dixon RE, Dobrev D, Gomez AM, Harraz OF, Hegyi B, Jones DK, Krogh-Madsen T, Murfee WL, Nystoriak MA, Posnack NG, Ripplinger CM, Veeraraghavan R, Weinberg S. Diversity of cells and signals in the cardiovascular system. J Physiol 2023; 601:2547-2592. [PMID: 36744541 PMCID: PMC10313794 DOI: 10.1113/jp284011] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2022] [Accepted: 01/19/2023] [Indexed: 02/07/2023] Open
Abstract
This white paper is the outcome of the seventh UC Davis Cardiovascular Research Symposium on Systems Approach to Understanding Cardiovascular Disease and Arrhythmia. This biannual meeting aims to bring together leading experts in subfields of cardiovascular biomedicine to focus on topics of importance to the field. The theme of the 2022 Symposium was 'Cell Diversity in the Cardiovascular System, cell-autonomous and cell-cell signalling'. Experts in the field contributed their experimental and mathematical modelling perspectives and discussed emerging questions, controversies, and challenges in examining cell and signal diversity, co-ordination and interrelationships involved in cardiovascular function. This paper originates from the topics of formal presentations and informal discussions from the Symposium, which aimed to develop a holistic view of how the multiple cell types in the cardiovascular system integrate to influence cardiovascular function, disease progression and therapeutic strategies. The first section describes the major cell types (e.g. cardiomyocytes, vascular smooth muscle and endothelial cells, fibroblasts, neurons, immune cells, etc.) and the signals involved in cardiovascular function. The second section emphasizes the complexity at the subcellular, cellular and system levels in the context of cardiovascular development, ageing and disease. Finally, the third section surveys the technological innovations that allow the interrogation of this diversity and advancing our understanding of the integrated cardiovascular function and dysfunction.
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Affiliation(s)
- Eleonora Grandi
- Department of Pharmacology, University of California Davis, Davis, CA, USA
| | - Manuel F. Navedo
- Department of Pharmacology, University of California Davis, Davis, CA, USA
| | - Jeffrey J. Saucerman
- Department of Biomedical Engineering, University of Virginia, Charlottesville, VA, USA
| | - Donald M. Bers
- Department of Pharmacology, University of California Davis, Davis, CA, USA
| | - Nipavan Chiamvimonvat
- Department of Pharmacology, University of California Davis, Davis, CA, USA
- Department of Internal Medicine, University of California Davis, Davis, CA, USA
| | - Rose E. Dixon
- Department of Physiology and Membrane Biology, University of California Davis, Davis, CA, USA
| | - Dobromir Dobrev
- Institute of Pharmacology, West German Heart and Vascular Center, University Duisburg-Essen, Essen, Germany
- Department of Medicine, Montreal Heart Institute and Université de Montréal, Montréal, Canada
- Department of Molecular Physiology & Biophysics, Baylor College of Medicine, Houston, TX, USA
| | - Ana M. Gomez
- Signaling and Cardiovascular Pathophysiology-UMR-S 1180, INSERM, Université Paris-Saclay, Orsay, France
| | - Osama F. Harraz
- Department of Pharmacology, Larner College of Medicine, and Vermont Center for Cardiovascular and Brain Health, University of Vermont, Burlington, VT, USA
| | - Bence Hegyi
- Department of Pharmacology, University of California Davis, Davis, CA, USA
| | - David K. Jones
- Department of Pharmacology, University of Michigan Medical School, Ann Arbor, MI, USA
- Department of Internal Medicine, University of Michigan Medical School, Ann Arbor, MI, USA
| | - Trine Krogh-Madsen
- Department of Physiology & Biophysics, Weill Cornell Medicine, New York, New York, USA
| | - Walter Lee Murfee
- J. Crayton Pruitt Family Department of Biomedical Engineering, University of Florida, Gainesville, FL, USA
| | - Matthew A. Nystoriak
- Department of Medicine, Division of Environmental Medicine, Center for Cardiometabolic Science, University of Louisville, Louisville, KY, 40202, USA
| | - Nikki G. Posnack
- Department of Pediatrics, Department of Pharmacology and Physiology, The George Washington University, Washington, DC, USA
- Sheikh Zayed Institute for Pediatric and Surgical Innovation, Children’s National Heart Institute, Children’s National Hospital, Washington, DC, USA
| | | | - Rengasayee Veeraraghavan
- Department of Biomedical Engineering, The Ohio State University, Columbus, OH, USA
- Dorothy M. Davis Heart & Lung Research Institute, The Ohio State University – Wexner Medical Center, Columbus, OH, USA
| | - Seth Weinberg
- Department of Biomedical Engineering, The Ohio State University, Columbus, OH, USA
- Dorothy M. Davis Heart & Lung Research Institute, The Ohio State University – Wexner Medical Center, Columbus, OH, USA
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Agrawal A, Wang K, Polonchuk L, Cooper J, Hendrix M, Gavaghan DJ, Mirams GR, Clerx M. Models of the cardiac L-type calcium current: A quantitative review. WIREs Mech Dis 2023; 15:e1581. [PMID: 36028219 PMCID: PMC10078428 DOI: 10.1002/wsbm.1581] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2022] [Revised: 06/16/2022] [Accepted: 07/19/2022] [Indexed: 01/31/2023]
Abstract
The L-type calcium current (I CaL ) plays a critical role in cardiac electrophysiology, and models ofI CaL are vital tools to predict arrhythmogenicity of drugs and mutations. Five decades of measuring and modelingI CaL have resulted in several competing theories (encoded in mathematical equations). However, the introduction of new models has not typically been accompanied by a data-driven critical comparison with previous work, so that it is unclear which model is best suited for any particular application. In this review, we describe and compare 73 published mammalianI CaL models and use simulated experiments to show that there is a large variability in their predictions, which is not substantially diminished when grouping by species or other categories. We provide model code for 60 models, list major data sources, and discuss experimental and modeling work that will be required to reduce this huge list of competing theories and ultimately develop a community consensus model ofI CaL . This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Molecular and Cellular Physiology.
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Affiliation(s)
- Aditi Agrawal
- Computational Biology & Health Informatics, Department of Computer ScienceUniversity of OxfordOxfordUK
| | - Ken Wang
- Pharma Research and Early Development, Innovation Center BaselF. Hoffmann‐La Roche Ltd.BaselSwitzerland
| | - Liudmila Polonchuk
- Pharma Research and Early Development, Innovation Center BaselF. Hoffmann‐La Roche Ltd.BaselSwitzerland
| | - Jonathan Cooper
- Centre for Advanced Research ComputingUniversity College LondonLondonUK
| | - Maurice Hendrix
- Centre for Mathematical Medicine & Biology, School of Mathematical SciencesUniversity of NottinghamNottinghamUK
- Digital Research Service, Information SciencesUniversity of NottinghamNottinghamUK
| | - David J. Gavaghan
- Computational Biology & Health Informatics, Department of Computer ScienceUniversity of OxfordOxfordUK
| | - Gary R. Mirams
- Centre for Mathematical Medicine & Biology, School of Mathematical SciencesUniversity of NottinghamNottinghamUK
| | - Michael Clerx
- Centre for Mathematical Medicine & Biology, School of Mathematical SciencesUniversity of NottinghamNottinghamUK
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6
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Qu Z, Yan D, Song Z. Modeling Calcium Cycling in the Heart: Progress, Pitfalls, and Challenges. Biomolecules 2022; 12:1686. [PMID: 36421700 PMCID: PMC9687412 DOI: 10.3390/biom12111686] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2022] [Revised: 11/08/2022] [Accepted: 11/11/2022] [Indexed: 11/16/2022] Open
Abstract
Intracellular calcium (Ca) cycling in the heart plays key roles in excitation-contraction coupling and arrhythmogenesis. In cardiac myocytes, the Ca release channels, i.e., the ryanodine receptors (RyRs), are clustered in the sarcoplasmic reticulum membrane, forming Ca release units (CRUs). The RyRs in a CRU act collectively to give rise to discrete Ca release events, called Ca sparks. A cell contains hundreds to thousands of CRUs, diffusively coupled via Ca to form a CRU network. A rich spectrum of spatiotemporal Ca dynamics is observed in cardiac myocytes, including Ca sparks, spark clusters, mini-waves, persistent whole-cell waves, and oscillations. Models of different temporal and spatial scales have been developed to investigate these dynamics. Due to the complexities of the CRU network and the spatiotemporal Ca dynamics, it is challenging to model the Ca cycling dynamics in the cardiac system, particularly at the tissue sales. In this article, we review the progress of modeling of Ca cycling in cardiac systems from single RyRs to the tissue scale, the pros and cons of the current models and different modeling approaches, and the challenges to be tackled in the future.
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Affiliation(s)
- Zhilin Qu
- Department of Medicine, David Geffen School of Medicine, University of California, A2-237 CHS, 650 Charles E. Young Drive South, Los Angeles, CA 90095, USA
- Department of Computational Medicine, David Geffen School of Medicine, University of California, Los Angeles, CA 90095, USA
| | - Dasen Yan
- Peng Cheng Laboratory, Shenzhen 518066, China
| | - Zhen Song
- Peng Cheng Laboratory, Shenzhen 518066, China
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7
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Colman MA, Alvarez-Lacalle E, Echebarria B, Sato D, Sutanto H, Heijman J. Multi-Scale Computational Modeling of Spatial Calcium Handling From Nanodomain to Whole-Heart: Overview and Perspectives. Front Physiol 2022; 13:836622. [PMID: 35370783 PMCID: PMC8964409 DOI: 10.3389/fphys.2022.836622] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2021] [Accepted: 01/31/2022] [Indexed: 11/13/2022] Open
Abstract
Regulation of intracellular calcium is a critical component of cardiac electrophysiology and excitation-contraction coupling. The calcium spark, the fundamental element of the intracellular calcium transient, is initiated in specialized nanodomains which co-locate the ryanodine receptors and L-type calcium channels. However, calcium homeostasis is ultimately regulated at the cellular scale, by the interaction of spatially separated but diffusively coupled nanodomains with other sub-cellular and surface-membrane calcium transport channels with strong non-linear interactions; and cardiac electrophysiology and arrhythmia mechanisms are ultimately tissue-scale phenomena, regulated by the interaction of a heterogeneous population of coupled myocytes. Recent advances in imaging modalities and image-analysis are enabling the super-resolution reconstruction of the structures responsible for regulating calcium homeostasis, including the internal structure of nanodomains themselves. Extrapolating functional and imaging data from the nanodomain to the whole-heart is non-trivial, yet essential for translational insight into disease mechanisms. Computational modeling has important roles to play in relating structural and functional data at the sub-cellular scale and translating data across the scales. This review covers recent methodological advances that enable image-based modeling of the single nanodomain and whole cardiomyocyte, as well as the development of multi-scale simulation approaches to integrate data from nanometer to whole-heart. Firstly, methods to overcome the computational challenges of simulating spatial calcium dynamics in the nanodomain are discussed, including image-based modeling at this scale. Then, recent whole-cell models, capable of capturing a range of different structures (such as the T-system and mitochondria) and cellular heterogeneity/variability are discussed at two different levels of discretization. Novel methods to integrate the models and data across the scales and simulate stochastic dynamics in tissue-scale models are then discussed, enabling elucidation of the mechanisms by which nanodomain remodeling underlies arrhythmia and contractile dysfunction. Perspectives on model differences and future directions are provided throughout.
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Affiliation(s)
- Michael A. Colman
- School of Biomedical Sciences, University of Leeds, Leeds, United Kingdom
- *Correspondence: Michael A. Colman,
| | | | - Blas Echebarria
- Departament de Fisica, Universitat Politècnica de Catalunya-BarcelonaTech, Barcelona, Spain
| | - Daisuke Sato
- Department of Pharmacology, School of Medicine, University of California, Davis, Davis, CA, United States
| | - Henry Sutanto
- Department of Physiology and Pharmacology, State University of New York Downstate Health Sciences University, Brooklyn, NY, United States
- Department of Cardiology, Cardiovascular Research Institute Maastricht, Maastricht University, Maastricht, Netherlands
| | - Jordi Heijman
- Department of Cardiology, Cardiovascular Research Institute Maastricht, Maastricht University, Maastricht, Netherlands
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8
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Louch WE, Perdreau-Dahl H, Edwards AG. Image-Driven Modeling of Nanoscopic Cardiac Function: Where Have We Come From, and Where Are We Going? Front Physiol 2022; 13:834211. [PMID: 35356084 PMCID: PMC8959215 DOI: 10.3389/fphys.2022.834211] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2021] [Accepted: 01/31/2022] [Indexed: 11/24/2022] Open
Abstract
Complementary developments in microscopy and mathematical modeling have been critical to our understanding of cardiac excitation–contraction coupling. Historically, limitations imposed by the spatial or temporal resolution of imaging methods have been addressed through careful mathematical interrogation. Similarly, limitations imposed by computational power have been addressed by imaging macroscopic function in large subcellular domains or in whole myocytes. As both imaging resolution and computational tractability have improved, the two approaches have nearly merged in terms of the scales that they can each be used to interrogate. With this review we will provide an overview of these advances and their contribution to understanding ventricular myocyte function, including exciting developments over the last decade. We specifically focus on experimental methods that have pushed back limits of either spatial or temporal resolution of nanoscale imaging (e.g., DNA-PAINT), or have permitted high resolution imaging on large cellular volumes (e.g., serial scanning electron microscopy). We also review the progression of computational approaches used to integrate and interrogate these new experimental data sources, and comment on near-term advances that may unify understanding of the underlying biology. Finally, we comment on several outstanding questions in cardiac physiology that stand to benefit from a concerted and complementary application of these new experimental and computational methods.
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Affiliation(s)
- William E. Louch
- Institute for Experimental Medical Research, Oslo University Hospital and University of Oslo, Oslo, Norway
- K.G. Jebsen Centre for Cardiac Research, University of Oslo, Oslo, Norway
| | - Harmonie Perdreau-Dahl
- Institute for Experimental Medical Research, Oslo University Hospital and University of Oslo, Oslo, Norway
- K.G. Jebsen Centre for Cardiac Research, University of Oslo, Oslo, Norway
| | - Andrew G. Edwards
- Simula Research Laboratory, Lysaker, Norway
- *Correspondence: Andrew G. Edwards,
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9
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Laasmaa M, Branovets J, Barsunova K, Karro N, Lygate CA, Birkedal R, Vendelin M. Altered calcium handling in cardiomyocytes from arginine-glycine amidinotransferase-knockout mice is rescued by creatine. Am J Physiol Heart Circ Physiol 2021; 320:H805-H825. [PMID: 33275525 DOI: 10.1152/ajpheart.00300.2020] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 04/28/2020] [Revised: 10/30/2020] [Accepted: 11/23/2020] [Indexed: 01/14/2023]
Abstract
The creatine kinase system facilitates energy transfer between mitochondria and the major ATPases in the heart. Creatine-deficient mice, which lack arginine-glycine amidinotransferase (AGAT) to synthesize creatine and homoarginine, exhibit reduced cardiac contractility. We studied how the absence of a functional CK system influences calcium handling in isolated cardiomyocytes from AGAT-knockouts and wild-type littermates as well as in AGAT-knockout mice receiving lifelong creatine supplementation via the food. Using a combination of whole cell patch clamp and fluorescence microscopy, we demonstrate that the L-type calcium channel (LTCC) current amplitude and voltage range of activation were significantly lower in AGAT-knockout compared with wild-type littermates. Additionally, the inactivation of LTCC and the calcium transient decay were significantly slower. According to our modeling results, these changes can be reproduced by reducing three parameters in knockout mice when compared with wild-type: LTCC conductance, the exchange constant of Ca2+ transfer between subspace and cytosol, and SERCA activity. Because tissue expression of LTCC and SERCA protein were not significantly different between genotypes, this suggests the involvement of posttranslational regulatory mechanisms or structural reorganization. The AGAT-knockout phenotype of calcium handling was fully reversed by dietary creatine supplementation throughout life. Our results indicate reduced calcium cycling in cardiomyocytes from AGAT-knockouts and suggest that the creatine kinase system is important for the development of calcium handling in the heart.NEW & NOTEWORTHY Creatine-deficient mice lacking arginine-glycine amidinotransferase exhibit compromised cardiac function. Here, we show that this is at least partially due to an overall slowing of calcium dynamics. Calcium influx into the cytosol via the L-type calcium current (LTCC) is diminished, and the rate of the sarcoendoplasmic reticulum calcium ATPase (SERCA) pumping calcium back into the sarcoplasmic reticulum is slower. The expression of LTCC and SERCA did not change, suggesting that the changes are regulatory.
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Affiliation(s)
- Martin Laasmaa
- Laboratory of Systems Biology, Department of Cybernetics, School of Science, Tallinn University of Technology, Tallinn, Estonia
| | - Jelena Branovets
- Laboratory of Systems Biology, Department of Cybernetics, School of Science, Tallinn University of Technology, Tallinn, Estonia
| | - Karina Barsunova
- Laboratory of Systems Biology, Department of Cybernetics, School of Science, Tallinn University of Technology, Tallinn, Estonia
| | - Niina Karro
- Laboratory of Systems Biology, Department of Cybernetics, School of Science, Tallinn University of Technology, Tallinn, Estonia
| | - Craig A Lygate
- Division of Cardiovascular Medicine, Radcliffe Department of Medicine, and the British Heart Foundation Centre of Research Excellence, University of Oxford, Tallinn, United Kingdom
| | - Rikke Birkedal
- Laboratory of Systems Biology, Department of Cybernetics, School of Science, Tallinn University of Technology, Tallinn, Estonia
| | - Marko Vendelin
- Laboratory of Systems Biology, Department of Cybernetics, School of Science, Tallinn University of Technology, Tallinn, Estonia
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Ca 2+ Release via IP 3 Receptors Shapes the Cardiac Ca 2+ Transient for Hypertrophic Signaling. Biophys J 2020; 119:1178-1192. [PMID: 32871099 DOI: 10.1016/j.bpj.2020.08.001] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2020] [Revised: 06/16/2020] [Accepted: 08/04/2020] [Indexed: 12/27/2022] Open
Abstract
Calcium (Ca2+) plays a central role in mediating both contractile function and hypertrophic signaling in ventricular cardiomyocytes. L-type Ca2+ channels trigger release of Ca2+ from ryanodine receptors for cellular contraction, whereas signaling downstream of G-protein-coupled receptors stimulates Ca2+ release via inositol 1,4,5-trisphosphate receptors (IP3Rs), engaging hypertrophic signaling pathways. Modulation of the amplitude, duration, and duty cycle of the cytosolic Ca2+ contraction signal and spatial localization have all been proposed to encode this hypertrophic signal. Given current knowledge of IP3Rs, we develop a model describing the effect of functional interaction (cross talk) between ryanodine receptor and IP3R channels on the Ca2+ transient and examine the sensitivity of the Ca2+ transient shape to properties of IP3R activation. A key result of our study is that IP3R activation increases Ca2+ transient duration for a broad range of IP3R properties, but the effect of IP3R activation on Ca2+ transient amplitude is dependent on IP3 concentration. Furthermore we demonstrate that IP3-mediated Ca2+ release in the cytosol increases the duty cycle of the Ca2+ transient, the fraction of the cycle for which [Ca2+] is elevated, across a broad range of parameter values and IP3 concentrations. When coupled to a model of downstream transcription factor (NFAT) activation, we demonstrate that there is a high correspondence between the Ca2+ transient duty cycle and the proportion of activated NFAT in the nucleus. These findings suggest increased cytosolic Ca2+ duty cycle as a plausible mechanism for IP3-dependent hypertrophic signaling via Ca2+-sensitive transcription factors such as NFAT in ventricular cardiomyocytes.
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11
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Cardiomyocyte calcium handling in health and disease: Insights from in vitro and in silico studies. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2020; 157:54-75. [PMID: 32188566 DOI: 10.1016/j.pbiomolbio.2020.02.008] [Citation(s) in RCA: 63] [Impact Index Per Article: 15.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2019] [Revised: 12/31/2019] [Accepted: 02/29/2020] [Indexed: 02/07/2023]
Abstract
Calcium (Ca2+) plays a central role in cardiomyocyte excitation-contraction coupling. To ensure an optimal electrical impulse propagation and cardiac contraction, Ca2+ levels are regulated by a variety of Ca2+-handling proteins. In turn, Ca2+ modulates numerous electrophysiological processes. Accordingly, Ca2+-handling abnormalities can promote cardiac arrhythmias via various mechanisms, including the promotion of afterdepolarizations, ion-channel modulation and structural remodeling. In the last 30 years, significant improvements have been made in the computational modeling of cardiomyocyte Ca2+ handling under physiological and pathological conditions. However, numerous questions involving the Ca2+-dependent regulation of different macromolecular complexes, cross-talk between Ca2+-dependent regulatory pathways operating over a wide range of time scales, and bidirectional interactions between electrophysiology and mechanics remain to be addressed by in vitro and in silico studies. A better understanding of disease-specific Ca2+-dependent proarrhythmic mechanisms may facilitate the development of improved therapeutic strategies. In this review, we describe the fundamental mechanisms of cardiomyocyte Ca2+ handling in health and disease, and provide an overview of currently available computational models for cardiomyocyte Ca2+ handling. Finally, we discuss important uncertainties and open questions about cardiomyocyte Ca2+ handling and highlight how synergy between in vitro and in silico studies may help to answer several of these issues.
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12
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Simulation Strategies for Calcium Microdomains and Calcium Noise. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2020; 1131:771-797. [DOI: 10.1007/978-3-030-12457-1_31] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
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13
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Lei CL, Clerx M, Beattie KA, Melgari D, Hancox JC, Gavaghan DJ, Polonchuk L, Wang K, Mirams GR. Rapid Characterization of hERG Channel Kinetics II: Temperature Dependence. Biophys J 2019; 117:2455-2470. [PMID: 31451180 PMCID: PMC6990152 DOI: 10.1016/j.bpj.2019.07.030] [Citation(s) in RCA: 30] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2019] [Revised: 06/20/2019] [Accepted: 07/17/2019] [Indexed: 11/29/2022] Open
Abstract
Ion channel behavior can depend strongly on temperature, with faster kinetics at physiological temperatures leading to considerable changes in currents relative to room temperature. These temperature-dependent changes in voltage-dependent ion channel kinetics (rates of opening, closing, inactivating, and recovery) are commonly represented with Q10 coefficients or an Eyring relationship. In this article, we assess the validity of these representations by characterizing channel kinetics at multiple temperatures. We focus on the human Ether-à-go-go-Related Gene (hERG) channel, which is important in drug safety assessment and commonly screened at room temperature so that results require extrapolation to physiological temperature. In Part I of this study, we established a reliable method for high-throughput characterization of hERG1a (Kv11.1) kinetics, using a 15-second information-rich optimized protocol. In this Part II, we use this protocol to study the temperature dependence of hERG kinetics using Chinese hamster ovary cells overexpressing hERG1a on the Nanion SyncroPatch 384PE, a 384-well automated patch-clamp platform, with temperature control. We characterize the temperature dependence of hERG gating by fitting the parameters of a mathematical model of hERG kinetics to data obtained at five distinct temperatures between 25 and 37°C and validate the models using different protocols. Our models reveal that activation is far more temperature sensitive than inactivation, and we observe that the temperature dependency of the kinetic parameters is not represented well by Q10 coefficients; it broadly follows a generalized, but not the standardly-used, Eyring relationship. We also demonstrate that experimental estimations of Q10 coefficients are protocol dependent. Our results show that a direct fit using our 15-s protocol best represents hERG kinetics at any given temperature and suggests that using the Generalized Eyring theory is preferable if no experimental data are available to derive model parameters at a given temperature.
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Affiliation(s)
- Chon Lok Lei
- Computational Biology, Department of Computer Science, University of Oxford, Oxford, United Kingdom
| | - Michael Clerx
- Computational Biology, Department of Computer Science, University of Oxford, Oxford, United Kingdom
| | - Kylie A Beattie
- Computational Biology, Department of Computer Science, University of Oxford, Oxford, United Kingdom
| | - Dario Melgari
- School of Physiology, Pharmacology and Neuroscience, and Cardiovascular Research Laboratories, School of Medical Sciences, University of Bristol, Bristol, United Kingdom
| | - Jules C Hancox
- School of Physiology, Pharmacology and Neuroscience, and Cardiovascular Research Laboratories, School of Medical Sciences, University of Bristol, Bristol, United Kingdom
| | - David J Gavaghan
- Computational Biology, Department of Computer Science, University of Oxford, Oxford, United Kingdom
| | - Liudmila Polonchuk
- Pharma Research and Early Development, Innovation Center Basel, F. Hoffmann-La Roche, Basel, Switzerland
| | - Ken Wang
- Pharma Research and Early Development, Innovation Center Basel, F. Hoffmann-La Roche, Basel, Switzerland
| | - Gary R Mirams
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom.
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14
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Chu L, Greenstein JL, Winslow RL. Na + microdomains and sparks: Role in cardiac excitation-contraction coupling and arrhythmias in ankyrin-B deficiency. J Mol Cell Cardiol 2019; 128:145-157. [PMID: 30731085 DOI: 10.1016/j.yjmcc.2019.02.001] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 06/06/2018] [Revised: 02/01/2019] [Accepted: 02/02/2019] [Indexed: 01/25/2023]
Abstract
Cardiac sodium (Na+) potassium ATPase (NaK) pumps, neuronal sodium channels (INa), and sodium calcium (Ca2+) exchangers (NCX1) may co-localize to form a Na+ microdomain. It remains controversial as to whether neuronal INa contributes to local Na+ accumulation, resulting in reversal of nearby NCX1 and influx of Ca2+ into the cell. Therefore, there has been great interest in the possible roles of a Na+ microdomain in cardiac Ca2+-induced Ca2+ release (CICR). In addition, the important role of co-localization of NaK and NCX1 in regulating localized Na+ and Ca2+ levels and CICR in ankyrin-B deficient (ankyrin-B+/-) cardiomyocytes has been examined in many recent studies. Altered Na+ dynamics may contribute to the appearance of arrhythmias, but the mechanisms underlying this relationship remain unclear. In order to investigate this, we present a mechanistic canine cardiomyocyte model which reproduces independent local dyadic junctional SR (JSR) Ca2+ release events underlying cell-wide excitation-contraction coupling, as well as a three-dimensional super-resolution model of the Ca2+ spark that describes local Na+ dynamics as governed by NaK pumps, neuronal INa, and NCX1. The model predicts the existence of Na+ sparks, which are generated by NCX1 and exhibit significantly slower dynamics as compared to Ca2+ sparks. Moreover, whole-cell simulations indicate that neuronal INa in the cardiac dyad plays a key role during the systolic phase. Rapid inward neuronal INa can elevate dyadic [Na+] to 35-40 mM, which drives reverse-mode NCX1 transport, and therefore promotes Ca2+ entry into the dyad, enhancing the trigger for JSR Ca2+ release. The specific role of decreased co-localization of NaK and NCX1 in ankyrin-B+/- cardiomyocytes was examined. Model results demonstrate that a reduction in the local NCX1- and NaK-mediated regulation of dyadic [Ca2+] and [Na+] results in an increase in Ca2+ spark activity during isoproterenol stimulation, which in turn stochastically activates NCX1 in the dyad. This alteration in NCX1/NaK co-localization interrupts the balance between NCX1 and NaK currents in a way that leads to enhanced depolarizing inward current during the action potential plateau, which ultimately leads to a higher probability of L-type Ca2+ channel reopening and arrhythmogenic early-afterdepolarizations.
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Affiliation(s)
- Lulu Chu
- Department of Biomedical Engineering and the Institute for Computational Medicine, The Johns Hopkins University School of Medicine and Whiting School of Engineering, 3400 N Charles Street, Baltimore, MD 21218, USA.
| | - Joseph L Greenstein
- Department of Biomedical Engineering and the Institute for Computational Medicine, The Johns Hopkins University School of Medicine and Whiting School of Engineering, 3400 N Charles Street, Baltimore, MD 21218, USA.
| | - Raimond L Winslow
- Department of Biomedical Engineering and the Institute for Computational Medicine, The Johns Hopkins University School of Medicine and Whiting School of Engineering, 3400 N Charles Street, Baltimore, MD 21218, USA.
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15
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Limpitikul WB, Greenstein JL, Yue DT, Dick IE, Winslow RL. A bilobal model of Ca 2+-dependent inactivation to probe the physiology of L-type Ca 2+ channels. J Gen Physiol 2018; 150:1688-1701. [PMID: 30470716 PMCID: PMC6279366 DOI: 10.1085/jgp.201812115] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2018] [Revised: 08/01/2018] [Accepted: 10/26/2018] [Indexed: 12/20/2022] Open
Abstract
L-type calcium channels undergo Ca2+-dependent inactivation (CDI) in order to precisely control the entry of Ca2+ into cells such as cardiomyocytes. Limpitikul et al. develop a bilobal model of CDI and use it to understand the pathogenesis of arrhythmias associated with mutations in CaM. L-type calcium channels (LTCCs) are critical elements of normal cardiac function, playing a major role in orchestrating cardiac electrical activity and initiating downstream signaling processes. LTCCs thus use feedback mechanisms to precisely control calcium (Ca2+) entry into cells. Of these, Ca2+-dependent inactivation (CDI) is significant because it shapes cardiac action potential duration and is essential for normal cardiac rhythm. This important form of regulation is mediated by a resident Ca2+ sensor, calmodulin (CaM), which is comprised of two lobes that are each capable of responding to spatially distinct Ca2+ sources. Disruption of CaM-mediated CDI leads to severe forms of long-QT syndrome (LQTS) and life-threatening arrhythmias. Thus, a model capable of capturing the nuances of CaM-mediated CDI would facilitate increased understanding of cardiac (patho)physiology. However, one critical barrier to achieving a detailed kinetic model of CDI has been the lack of quantitative data characterizing CDI as a function of Ca2+. This data deficit stems from the experimental challenge of uncoupling the effect of channel gating on Ca2+ entry. To overcome this obstacle, we use photo-uncaging of Ca2+ to deliver a measurable Ca2+ input to CaM/LTCCs, while simultaneously recording CDI. Moreover, we use engineered CaMs with Ca2+ binding restricted to a single lobe, to isolate the kinetic response of each lobe. These high-resolution measurements enable us to build mathematical models for each lobe of CaM, which we use as building blocks for a full-scale bilobal model of CDI. Finally, we use this model to probe the pathogenesis of LQTS associated with mutations in CaM (calmodulinopathies). Each of these models accurately recapitulates the kinetics and steady-state properties of CDI in both physiological and pathological states, thus offering powerful new insights into the mechanistic alterations underlying cardiac arrhythmias.
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Affiliation(s)
- Worawan B Limpitikul
- Calcium Signals Laboratory, Department of Biomedical Engineering, The Johns Hopkins University School of Medicine, Baltimore, MD
| | - Joseph L Greenstein
- Institute for Computational Medicine, Department of Biomedical Engineering, The Johns Hopkins University, Baltimore, MD
| | - David T Yue
- Calcium Signals Laboratory, Department of Biomedical Engineering, The Johns Hopkins University School of Medicine, Baltimore, MD
| | - Ivy E Dick
- Calcium Signals Laboratory, Department of Biomedical Engineering, The Johns Hopkins University School of Medicine, Baltimore, MD .,Department of Physiology, University of Maryland School of Medicine, Baltimore, MD
| | - Raimond L Winslow
- Institute for Computational Medicine, Department of Biomedical Engineering, The Johns Hopkins University, Baltimore, MD
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16
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Walker MA, Gurev V, Rice JJ, Greenstein JL, Winslow RL. Estimating the probabilities of rare arrhythmic events in multiscale computational models of cardiac cells and tissue. PLoS Comput Biol 2017; 13:e1005783. [PMID: 29145393 PMCID: PMC5689829 DOI: 10.1371/journal.pcbi.1005783] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2017] [Accepted: 09/18/2017] [Indexed: 11/24/2022] Open
Abstract
Ectopic heartbeats can trigger reentrant arrhythmias, leading to ventricular fibrillation and sudden cardiac death. Such events have been attributed to perturbed Ca2+ handling in cardiac myocytes leading to spontaneous Ca2+ release and delayed afterdepolarizations (DADs). However, the ways in which perturbation of specific molecular mechanisms alters the probability of ectopic beats is not understood. We present a multiscale model of cardiac tissue incorporating a biophysically detailed three-dimensional model of the ventricular myocyte. This model reproduces realistic Ca2+ waves and DADs driven by stochastic Ca2+ release channel (RyR) gating and is used to study mechanisms of DAD variability. In agreement with previous experimental and modeling studies, key factors influencing the distribution of DAD amplitude and timing include cytosolic and sarcoplasmic reticulum Ca2+ concentrations, inwardly rectifying potassium current (IK1) density, and gap junction conductance. The cardiac tissue model is used to investigate how random RyR gating gives rise to probabilistic triggered activity in a one-dimensional myocyte tissue model. A novel spatial-average filtering method for estimating the probability of extreme (i.e. rare, high-amplitude) stochastic events from a limited set of spontaneous Ca2+ release profiles is presented. These events occur when randomly organized clusters of cells exhibit synchronized, high amplitude Ca2+ release flux. It is shown how reduced IK1 density and gap junction coupling, as observed in heart failure, increase the probability of extreme DADs by multiple orders of magnitude. This method enables prediction of arrhythmia likelihood and its modulation by alterations of other cellular mechanisms.
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Affiliation(s)
- Mark A. Walker
- Department of Biomedical Engineering and Institute for Computational Medicine, Johns Hopkins University, Baltimore, MD, United States of America
| | - Viatcheslav Gurev
- TJ Watson Research Center, IBM, Yorktown Heights, NY, United States of America
| | - John J. Rice
- TJ Watson Research Center, IBM, Yorktown Heights, NY, United States of America
| | - Joseph L. Greenstein
- Department of Biomedical Engineering and Institute for Computational Medicine, Johns Hopkins University, Baltimore, MD, United States of America
| | - Raimond L. Winslow
- Department of Biomedical Engineering and Institute for Computational Medicine, Johns Hopkins University, Baltimore, MD, United States of America
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17
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Ji H, Li Y, Weinberg SH. Calcium Ion Fluctuations Alter Channel Gating in a Stochastic Luminal Calcium Release Site Model. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2017; 14:611-619. [PMID: 26561478 DOI: 10.1109/tcbb.2015.2498552] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Stochasticity and small system size effects in complex biochemical reaction networks can greatly alter transient and steady-state system properties. A common approach to modeling reaction networks, which accounts for system size, is the chemical master equation that governs the dynamics of the joint probability distribution for molecular copy number. However, calculation of the stationary distribution is often prohibitive, due to the large state-space associated with most biochemical reaction networks. Here, we analyze a network representing a luminal calcium release site model and investigate to what extent small system size effects and calcium fluctuations, driven by ion channel gating, influx and diffusion, alter steady-state ion channel properties including open probability. For a physiological ion channel gating model and number of channels, the state-space may be between approximately 106-108 elements, and a novel modified block power method is used to solve the associated dominant eigenvector problem required to calculate the stationary distribution. We demonstrate that both small local cytosolic domain volume and a small number of ion channels drive calcium fluctuations that result in deviation from the corresponding model that neglects small system size effects.
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18
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Zhao CY, Greenstein JL, Winslow RL. Mechanisms of the cyclic nucleotide cross-talk signaling network in cardiac L-type calcium channel regulation. J Mol Cell Cardiol 2017; 106:29-44. [PMID: 28365422 PMCID: PMC5508987 DOI: 10.1016/j.yjmcc.2017.01.013] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 10/26/2016] [Revised: 12/16/2016] [Accepted: 01/20/2017] [Indexed: 10/19/2022]
Abstract
Regulation of L-type Calcium (Ca2+) Channel (LCC) gating is critical to shaping the cardiac action potential (AP) and triggering the initiation of excitation-contraction (EC) coupling in cardiac myocytes. The cyclic nucleotide (cN) cross-talk signaling network, which encompasses the β-adrenergic and the Nitric Oxide (NO)/cGMP/Protein Kinase G (PKG) pathways and their interaction (cross-talk) through distinctively-regulated phosphodiesterase isoenzymes (PDEs), regulates LCC current via Protein Kinase A- (PKA) and PKG-mediated phosphorylation. Due to the tightly-coupled and intertwined biochemical reactions involved, it remains to be clarified how LCC gating is regulated by the signaling network from receptor to end target. In addition, the large number of EC coupling-related phosphorylation targets of PKA and PKG makes it difficult to quantify and isolate changes in L-type Ca2+ current (ICaL) responses regulated by the signaling network. We have developed a multi-scale, biophysically-detailed computational model of LCC regulation by the cN signaling network that is supported by experimental data. LCCs are modeled with functionally distinct PKA- and PKG-phosphorylation dependent gating modes. The model exhibits experimentally observed single channel characteristics, as well as whole-cell LCC currents upon activation of the cross-talk signaling network. Simulations show 1) redistribution of LCC gating modes explains changes in whole-cell current under various stimulation scenarios of the cN cross-talk network; 2) NO regulation occurs via potentiation of a gating mode characterized by prolonged closed times; and 3) due to compensatory actions of cross-talk and antagonizing functions of PKA- and PKG-mediated phosphorylation of LCCs, the effects of individual inhibitions of PDEs 2, 3, and 4 on ICaL are most pronounced at low levels of β-adrenergic stimulation. Simulations also delineate the contribution of the following two mechanisms to overall LCC regulation, which have otherwise been challenging to distinguish: 1) regulation of PKA and PKG activation via cN cross-talk (Mechanism 1); and 2) LCC interaction with activated PKA and PKG (Mechanism 2). These results provide insights into how cN signals transduced via the cN cross-talk signaling network are integrated via LCC regulation in the heart.
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Affiliation(s)
- Claire Y Zhao
- Department of Biomedical Engineering and the Institute for Computational Medicine, The Johns Hopkins University School of Medicine and Whiting School of Engineering, 3400 N Charles Street, Baltimore, MD, 21218, USA.
| | - Joseph L Greenstein
- Department of Biomedical Engineering and the Institute for Computational Medicine, The Johns Hopkins University School of Medicine and Whiting School of Engineering, 3400 N Charles Street, Baltimore, MD, 21218, USA.
| | - Raimond L Winslow
- Department of Biomedical Engineering and the Institute for Computational Medicine, The Johns Hopkins University School of Medicine and Whiting School of Engineering, 3400 N Charles Street, Baltimore, MD, 21218, USA.
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19
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Maleckar MM, Edwards AG, Louch WE, Lines GT. Studying dyadic structure-function relationships: a review of current modeling approaches and new insights into Ca 2+ (mis)handling. CLINICAL MEDICINE INSIGHTS-CARDIOLOGY 2017; 11:1179546817698602. [PMID: 28469494 PMCID: PMC5392018 DOI: 10.1177/1179546817698602] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 06/30/2016] [Accepted: 12/19/2016] [Indexed: 11/25/2022]
Abstract
Excitation–contraction coupling in cardiac myocytes requires calcium influx through L-type calcium channels in the sarcolemma, which gates calcium release through sarcoplasmic reticulum ryanodine receptors in a process known as calcium-induced calcium release, producing a myoplasmic calcium transient and enabling cardiomyocyte contraction. The spatio-temporal dynamics of calcium release, buffering, and reuptake into the sarcoplasmic reticulum play a central role in excitation–contraction coupling in both normal and diseased cardiac myocytes. However, further quantitative understanding of these cells’ calcium machinery and the study of mechanisms that underlie both normal cardiac function and calcium-dependent etiologies in heart disease requires accurate knowledge of cardiac ultrastructure, protein distribution and subcellular function. As current imaging techniques are limited in spatial resolution, limiting insight into changes in calcium handling, computational models of excitation–contraction coupling have been increasingly employed to probe these structure–function relationships. This review will focus on the development of structural models of cardiac calcium dynamics at the subcellular level, orienting the reader broadly towards the development of models of subcellular calcium handling in cardiomyocytes. Specific focus will be given to progress in recent years in terms of multi-scale modeling employing resolved spatial models of subcellular calcium machinery. A review of the state-of-the-art will be followed by a review of emergent insights into calcium-dependent etiologies in heart disease and, finally, we will offer a perspective on future directions for related computational modeling and simulation efforts.
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Affiliation(s)
- Mary M Maleckar
- Simula Research Laboratory, Center for Cardiological Innovation and Center for Biomedical Computing, Lysaker, Norway
| | - Andrew G Edwards
- Simula Research Laboratory, Center for Cardiological Innovation and Center for Biomedical Computing, Lysaker, Norway.,University of Oslo, Oslo, Norway
| | - William E Louch
- Institute for Experimental Medical Research (IEMR), Oslo University Hospital and the University of Oslo, Oslo, Norway
| | - Glenn T Lines
- Simula Research Laboratory, Center for Cardiological Innovation and Center for Biomedical Computing, Lysaker, Norway
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20
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Revealing calcium fluxes by analyzing inhibition dynamics in action potential clamp. J Mol Cell Cardiol 2016; 100:93-108. [DOI: 10.1016/j.yjmcc.2016.08.015] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 04/04/2016] [Revised: 07/19/2016] [Accepted: 08/22/2016] [Indexed: 11/29/2022]
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21
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Yang PC, Boras BW, Jeng MT, Docken SS, Lewis TJ, McCulloch AD, Harvey RD, Clancy CE. A Computational Modeling and Simulation Approach to Investigate Mechanisms of Subcellular cAMP Compartmentation. PLoS Comput Biol 2016; 12:e1005005. [PMID: 27409243 PMCID: PMC4943723 DOI: 10.1371/journal.pcbi.1005005] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2016] [Accepted: 05/26/2016] [Indexed: 11/18/2022] Open
Abstract
Subcellular compartmentation of the ubiquitous second messenger cAMP has been widely proposed as a mechanism to explain unique receptor-dependent functional responses. How exactly compartmentation is achieved, however, has remained a mystery for more than 40 years. In this study, we developed computational and mathematical models to represent a subcellular sarcomeric space in a cardiac myocyte with varying detail. We then used these models to predict the contributions of various mechanisms that establish subcellular cAMP microdomains. We used the models to test the hypothesis that phosphodiesterases act as functional barriers to diffusion, creating discrete cAMP signaling domains. We also used the models to predict the effect of a range of experimentally measured diffusion rates on cAMP compartmentation. Finally, we modeled the anatomical structures in a cardiac myocyte diad, to predict the effects of anatomical diffusion barriers on cAMP compartmentation. When we incorporated experimentally informed model parameters to reconstruct an in silico subcellular sarcomeric space with spatially distinct cAMP production sites linked to caveloar domains, the models predict that under realistic conditions phosphodiesterases alone were insufficient to generate significant cAMP gradients. This prediction persisted even when combined with slow cAMP diffusion. When we additionally considered the effects of anatomic barriers to diffusion that are expected in the cardiac myocyte dyadic space, cAMP compartmentation did occur, but only when diffusion was slow. Our model simulations suggest that additional mechanisms likely contribute to cAMP gradients occurring in submicroscopic domains. The difference between the physiological and pathological effects resulting from the production of cAMP may be a function of appropriate compartmentation of cAMP signaling. Therefore, understanding the contribution of factors that are responsible for coordinating the spatial and temporal distribution of cAMP at the subcellular level could be important for developing new strategies for the prevention or treatment of unfavorable responses associated with different disease states. Subcellular compartmentation of the ubiquitous second messenger cAMP has been widely proposed as a mechanism to explain how this one signaling molecule produces unique receptor-dependent functional responses. But, how exactly compartmentation occurs, is unknown. This is because there has been no way to measure the regulation and movement of cAMP in cells with intact subcellular structures. In this study, we applied novel computational approaches to predict whether PDE activity alone or in conjunction with restricted diffusion is sufficient to produce cAMP gradients in submicroscopic signaling domains. We also used the models to test the effect of a range of experimentally measured diffusion rates on cAMP compartmentation. Our simulations suggest that PDE activity alone is not sufficient to explain compartmentation, but if diffusion of cAMP is limited by potential factors such as molecular crowding, PKA buffering, and anatomical barriers, then compartmentation is predicted to occur.
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Affiliation(s)
- Pei-Chi Yang
- Department of Pharmacology, University of California Davis, Davis, California, United States of America
| | - Britton W. Boras
- Department of Biomedical Engineering, University of California San Diego, La Jolla, California, United States of America
| | - Mao-Tsuen Jeng
- Department of Pharmacology, University of California Davis, Davis, California, United States of America
| | - Steffen S. Docken
- Department of Pharmacology, University of California Davis, Davis, California, United States of America
- Department of Mathematics, University of California Davis, Davis, California, United States of America
| | - Timothy J. Lewis
- Department of Mathematics, University of California Davis, Davis, California, United States of America
- * E-mail: (TJL); (ADM); (RDH); (CEC)
| | - Andrew D. McCulloch
- Department of Biomedical Engineering, University of California San Diego, La Jolla, California, United States of America
- * E-mail: (TJL); (ADM); (RDH); (CEC)
| | - Robert D. Harvey
- Department of Pharmacology, Center for Molecular Medicine, School of Medicine, University of Nevada Reno, Reno, Nevada, United States of America
- * E-mail: (TJL); (ADM); (RDH); (CEC)
| | - Colleen E. Clancy
- Department of Pharmacology, University of California Davis, Davis, California, United States of America
- * E-mail: (TJL); (ADM); (RDH); (CEC)
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22
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A Computational Modeling and Simulation Approach to Investigate Mechanisms of Subcellular cAMP Compartmentation. PLoS Comput Biol 2016. [DOI: 10.1371/journal.pcbi.1005005 pcompbiol-d-16-00287] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
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23
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Chu L, Greenstein JL, Winslow RL. Modeling Na +-Ca 2+ exchange in the heart: Allosteric activation, spatial localization, sparks and excitation-contraction coupling. J Mol Cell Cardiol 2016; 99:174-187. [PMID: 27377851 DOI: 10.1016/j.yjmcc.2016.06.068] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 03/18/2016] [Revised: 06/14/2016] [Accepted: 06/30/2016] [Indexed: 01/19/2023]
Abstract
The cardiac sodium (Na+)/calcium (Ca2+) exchanger (NCX1) is an electrogenic membrane transporter that regulates Ca2+ homeostasis in cardiomyocytes, serving mainly to extrude Ca2+ during diastole. The direction of Ca2+ transport reverses at membrane potentials near that of the action potential plateau, generating an influx of Ca2+ into the cell. Therefore, there has been great interest in the possible roles of NCX1 in cardiac Ca2+-induced Ca2+ release (CICR). Interest has been reinvigorated by a recent super-resolution optical imaging study suggesting that ~18% of NCX1 co-localize with ryanodine receptor (RyR2) clusters, and ~30% of additional NCX1 are localized to within ~120nm of the nearest RyR2. NCX1 may therefore occupy a privileged position in which to modulate CICR. To examine this question, we have developed a mechanistic biophysically-detailed model of NCX1 that describes both NCX1 transport kinetics and Ca2+-dependent allosteric regulation. This NCX1 model was incorporated into a previously developed super-resolution model of the Ca2+ spark as well as a computational model of the cardiac ventricular myocyte that includes a detailed description of CICR with stochastic gating of L-type Ca2+ channels and RyR2s, and that accounts for local Ca2+ gradients near the dyad via inclusion of a peri-dyadic (PD) compartment. Both models predict that increasing the fraction of NCX1 in the dyad and PD decreases spark frequency, fidelity, and diastolic Ca2+ levels. Spark amplitude and duration are less sensitive to NCX1 spatial redistribution. On the other hand, NCX1 plays an important role in promoting Ca2+ entry into the dyad, and hence contributing to the trigger for RyR2 release at depolarized membrane potentials and in the presence of elevated local Na+ concentration. Whole-cell simulation of NCX1 tail currents are consistent with the finding that a relatively high fraction of NCX1 (~45%) resides in the dyadic and PD spaces, with a dyad-to-PD ratio of roughly 1:2. Allosteric Ca2+ activation of NCX1 helps to "functionally localize" exchanger activity to the dyad and PD by reducing exchanger activity in the cytosol thereby protecting the cell from excessive loss of Ca2+ during diastole.
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Affiliation(s)
- Lulu Chu
- Department of Biomedical Engineering and the Institute for Computational Medicine, The Johns Hopkins University School of Medicine and Whiting School of Engineering, 3400 N Charles Street, Baltimore, MD, 21218, USA.
| | - Joseph L Greenstein
- Department of Biomedical Engineering and the Institute for Computational Medicine, The Johns Hopkins University School of Medicine and Whiting School of Engineering, 3400 N Charles Street, Baltimore, MD, 21218, USA.
| | - Raimond L Winslow
- Department of Biomedical Engineering and the Institute for Computational Medicine, The Johns Hopkins University School of Medicine and Whiting School of Engineering, 3400 N Charles Street, Baltimore, MD, 21218, USA.
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24
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Gattoni S, Røe ÅT, Frisk M, Louch WE, Niederer SA, Smith NP. The calcium-frequency response in the rat ventricular myocyte: an experimental and modelling study. J Physiol 2016; 594:4193-224. [PMID: 26916026 DOI: 10.1113/jp272011] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2015] [Accepted: 02/22/2016] [Indexed: 12/11/2022] Open
Abstract
KEY POINTS In the majority of species, including humans, increased heart rate increases cardiac contractility. This change is known as the force-frequency response (FFR). The majority of mammals have a positive force-frequency relationship (FFR). In rat the FFR is controversial. We derive a species- and temperature-specific data-driven model of the rat ventricular myocyte. As a measure of the FFR, we test the effects of changes in frequency and extracellular calcium on the calcium-frequency response (CFR) in our model and three altered models. The results show a biphasic peak calcium-frequency response, due to biphasic behaviour of the ryanodine receptor and the combined effect of the rapid calmodulin buffer and the frequency-dependent increase in diastolic calcium. Alterations to the model reveal that inclusion of Ca(2+) /calmodulin-dependent protein kinase II (CAMKII)-mediated L-type channel and transient outward K(+) current activity enhances the positive magnitude calcium-frequency response, and the absence of CAMKII-mediated increase in activity of the sarco/endoplasmic reticulum Ca(2+) -ATPase induces a negative magnitude calcium-frequency response. ABSTRACT An increase in heart rate affects the strength of cardiac contraction by altering the Ca(2+) transient as a response to physiological demands. This is described by the force-frequency response (FFR), a change in developed force with pacing frequency. The majority of mammals, including humans, have a positive FFR, and cardiac contraction strength increases with heart rate. However, the rat and mouse are exceptions, with the majority of studies reporting a negative FFR, while others report either a biphasic or a positive FFR. Understanding the differences in the FFR between humans and rats is fundamental to interpreting rat-based experimental findings in the context of human physiology. We have developed a novel model of rat ventricular electrophysiology and calcium dynamics, derived predominantly from experimental data recorded under physiological conditions. As a measure of FFR, we tested the effects of changes in stimulation frequency and extracellular calcium concentration on the simulated Ca(2+) transient characteristics and showed a biphasic peak calcium-frequency relationship, consistent with recent observations of a shift from negative to positive FFR when approaching the rat physiological frequency range. We tested the hypotheses that (1) inhibition of Ca(2+) /calmodulin-dependent protein kinase II (CAMKII)-mediated increase in sarco/endoplasmic reticulum Ca(2+) -ATPase (SERCA) activity, (2) CAMKII modulation of SERCA, L-type channel and transient outward K(+) current activity and (3) Na(+) /K(+) pump dynamics play a significant role in the rat FFR. The results reveal a major role for CAMKII modulation of SERCA in the peak Ca(2+) -frequency response, driven most significantly by the cytosolic calcium buffering system and changes in diastolic Ca(2+) .
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Affiliation(s)
- Sara Gattoni
- King's College London, Department of Biomedical Engineering and Imaging Sciences, St. Thomas' Hospital, London, UK
| | - Åsmund Treu Røe
- Institute for Experimental Medical Research, Oslo University Hospital and University of Oslo, Oslo, Norway.,K. G. Jebsen Cardiac Research Center and Center for Heart Failure Research, University of Oslo, Oslo, Norway
| | - Michael Frisk
- Institute for Experimental Medical Research, Oslo University Hospital and University of Oslo, Oslo, Norway.,K. G. Jebsen Cardiac Research Center and Center for Heart Failure Research, University of Oslo, Oslo, Norway
| | - William E Louch
- Institute for Experimental Medical Research, Oslo University Hospital and University of Oslo, Oslo, Norway.,K. G. Jebsen Cardiac Research Center and Center for Heart Failure Research, University of Oslo, Oslo, Norway
| | - Steven A Niederer
- King's College London, Department of Biomedical Engineering and Imaging Sciences, St. Thomas' Hospital, London, UK
| | - Nicolas P Smith
- King's College London, Department of Biomedical Engineering and Imaging Sciences, St. Thomas' Hospital, London, UK.,University of Auckland, Engineering School Block 1, Level 5, 20 Symonds St, Auckland, 101, New Zealand
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25
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Walker MA, Williams GSB, Kohl T, Lehnart SE, Jafri MS, Greenstein JL, Lederer WJ, Winslow RL. Superresolution modeling of calcium release in the heart. Biophys J 2016; 107:3018-3029. [PMID: 25517166 PMCID: PMC4269784 DOI: 10.1016/j.bpj.2014.11.003] [Citation(s) in RCA: 79] [Impact Index Per Article: 9.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2014] [Revised: 10/20/2014] [Accepted: 11/04/2014] [Indexed: 12/29/2022] Open
Abstract
Stable calcium-induced calcium release (CICR) is critical for maintaining normal cellular contraction during cardiac excitation-contraction coupling. The fundamental element of CICR in the heart is the calcium (Ca2+) spark, which arises from a cluster of ryanodine receptors (RyR). Opening of these RyR clusters is triggered to produce a local, regenerative release of Ca2+ from the sarcoplasmic reticulum (SR). The Ca2+ leak out of the SR is an important process for cellular Ca2+ management, and it is critically influenced by spark fidelity, i.e., the probability that a spontaneous RyR opening triggers a Ca2+ spark. Here, we present a detailed, three-dimensional model of a cardiac Ca2+ release unit that incorporates diffusion, intracellular buffering systems, and stochastically gated ion channels. The model exhibits realistic Ca2+ sparks and robust Ca2+ spark termination across a wide range of geometries and conditions. Furthermore, the model captures the details of Ca2+ spark and nonspark-based SR Ca2+ leak, and it produces normal excitation-contraction coupling gain. We show that SR luminal Ca2+-dependent regulation of the RyR is not critical for spark termination, but it can explain the exponential rise in the SR Ca2+ leak-load relationship demonstrated in previous experimental work. Perturbations to subspace dimensions, which have been observed in experimental models of disease, strongly alter Ca2+ spark dynamics. In addition, we find that the structure of RyR clusters also influences Ca2+ release properties due to variations in inter-RyR coupling via local subspace Ca2+ concentration ([Ca2+]ss). These results are illustrated for RyR clusters based on super-resolution stimulated emission depletion microscopy. Finally, we present a believed-novel approach by which the spark fidelity of a RyR cluster can be predicted from structural information of the cluster using the maximum eigenvalue of its adjacency matrix. These results provide critical insights into CICR dynamics in heart, under normal and pathological conditions.
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Affiliation(s)
- Mark A Walker
- Institute for Computational Medicine, Department of Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland
| | - George S B Williams
- Center for Biomedical Engineering and Technology, University of Maryland School of Medicine, Baltimore, Maryland
| | - Tobias Kohl
- Heart Research Center Goettingen, Clinic of Cardiology and Pulmonology, University Medical Center Goettingen, Goettingen, Germany
| | - Stephan E Lehnart
- Heart Research Center Goettingen, Clinic of Cardiology and Pulmonology, University Medical Center Goettingen, Goettingen, Germany
| | - M Saleet Jafri
- Department of Molecular Neuroscience, Krasnow Institute for Advanced Study, George Mason University, Fairfax, Virginia
| | - Joseph L Greenstein
- Institute for Computational Medicine, Department of Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland
| | - W J Lederer
- Center for Biomedical Engineering and Technology, University of Maryland School of Medicine, Baltimore, Maryland
| | - Raimond L Winslow
- Institute for Computational Medicine, Department of Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland.
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26
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Electron tomography of rabbit cardiomyocyte three-dimensional ultrastructure. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2016; 121:77-84. [PMID: 27210305 PMCID: PMC4959512 DOI: 10.1016/j.pbiomolbio.2016.05.005] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/14/2016] [Accepted: 05/01/2016] [Indexed: 12/22/2022]
Abstract
The field of cardiovascular research has benefitted from rapid developments in imaging technology over the last few decades. Accordingly, an ever growing number of large, multidimensional data sets have begun to appear, often challenging existing pre-conceptions about structure and function of biological systems. For tissue and cell structure imaging, the move from 2D section-based microscopy to true 3D data collection has been a major driver of new insight. In the sub-cellular domain, electron tomography is a powerful technique for exploration of cellular structures in 3D with unparalleled fidelity at nanometer resolution. Electron tomography is particularly advantageous for studying highly compartmentalised cells such as cardiomyocytes, where elaborate sub-cellular structures play crucial roles in electrophysiology and mechanics. Although the anatomy of specific ultra-structures, such as dyadic couplons, has been extensively explored using 2D electron microscopy of thin sections, we still lack accurate, quantitative knowledge of true individual shape, volume and surface area of sub-cellular domains, as well as their 3D spatial interrelations; let alone of how these are reshaped during the cycle of contraction and relaxation. Here we discuss and illustrate the utility of ET for identification, visualisation, and analysis of 3D cardiomyocyte ultrastructures such as the T-tubular system, sarcoplasmic reticulum, mitochondria and microtubules.
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27
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Foteinou PT, Greenstein JL, Winslow RL. Mechanistic Investigation of the Arrhythmogenic Role of Oxidized CaMKII in the Heart. Biophys J 2016; 109:838-49. [PMID: 26287635 DOI: 10.1016/j.bpj.2015.06.064] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2014] [Revised: 05/16/2015] [Accepted: 06/30/2015] [Indexed: 10/23/2022] Open
Abstract
Oxidative stress and calcium (Ca(2+))/calmodulin (CaM)-dependent protein kinase II (CaMKII) both play important roles in the pathogenesis of cardiac disease. Although the pathophysiological relevance of reactive oxygen species (ROS) and CaMKII has been appreciated for some time, recent work has shown that ROS can directly oxidize CaMKII, leading to its persistent activity and an increase of the likelihood of cellular arrhythmias such as early afterdepolarizations (EADs). Because CaMKII modulates the function of many proteins involved in excitation-contraction coupling, elucidation of its role in cardiac function, in both healthy and oxidative stress conditions, is challenging. To investigate this role, we have developed a model of CaMKII activation that includes both the phosphorylation-dependent and the newly identified oxidation-dependent activation pathways. This model is incorporated into our previous local-control model of the cardiac myocyte that describes excitation-contraction coupling via stochastic simulation of individual Ca(2+) release units and CaMKII-mediated phosphorylation of L-type Ca(2+) channels (LCCs), ryanodine receptors and sodium (Na(+)) channels. The model predicts the experimentally measured slow-rate dependence of H2O2-induced EADs. Upon increased H2O2, simulations suggest that selective activation of late Na(+) current (INaL), although it prolongs action potential duration, is not by itself sufficient to produce EADs. Similar results are obtained if CaMKII effects on LCCs and ryanodine receptors are considered separately. However, EADs emerge upon simultaneous activation of both LCCs and Na(+) channels. Further modeling results implicate activation of the Na(+)-Ca(2+) exchanger (NCX) as an important player in the generation of EADs. During bradycardia, the emergence of H2O2-induced EADs was correlated with a shift in the timing of NCX current reversal toward the plateau phase earlier in the action potential. Using the timing of NCX current reversal as an indicator event for EADs, the model identified counterintuitive ionic changes-difficult to experimentally dissect-that have the greatest influence on ROS-related arrhythmia propensity.
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Affiliation(s)
- Panagiota T Foteinou
- Institute for Computational Medicine and Department of Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland
| | - Joseph L Greenstein
- Institute for Computational Medicine and Department of Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland
| | - Raimond L Winslow
- Institute for Computational Medicine and Department of Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland.
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28
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Himeno Y, Asakura K, Cha CY, Memida H, Powell T, Amano A, Noma A. A human ventricular myocyte model with a refined representation of excitation-contraction coupling. Biophys J 2016. [PMID: 26200878 DOI: 10.1016/j.bpj.2015.06.017] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022] Open
Abstract
Cardiac Ca(2+)-induced Ca(2+) release (CICR) occurs by a regenerative activation of ryanodine receptors (RyRs) within each Ca(2+)-releasing unit, triggered by the activation of L-type Ca(2+) channels (LCCs). CICR is then terminated, most probably by depletion of Ca(2+) in the junctional sarcoplasmic reticulum (SR). Hinch et al. previously developed a tightly coupled LCC-RyR mathematical model, known as the Hinch model, that enables simulations to deal with a variety of functional states of whole-cell populations of a Ca(2+)-releasing unit using a personal computer. In this study, we developed a membrane excitation-contraction model of the human ventricular myocyte, which we call the human ventricular cell (HuVEC) model. This model is a hybrid of the most recent HuVEC models and the Hinch model. We modified the Hinch model to reproduce the regenerative activation and termination of CICR. In particular, we removed the inactivated RyR state and separated the single step of RyR activation by LCCs into triggering and regenerative steps. More importantly, we included the experimental measurement of a transient rise in Ca(2+) concentrations ([Ca(2+)], 10-15 μM) during CICR in the vicinity of Ca(2+)-releasing sites, and thereby calculated the effects of the local Ca(2+) gradient on CICR as well as membrane excitation. This HuVEC model successfully reconstructed both membrane excitation and key properties of CICR. The time course of CICR evoked by an action potential was accounted for by autonomous changes in an instantaneous equilibrium open probability of couplons. This autonomous time course was driven by a core feedback loop including the pivotal local [Ca(2+)], influenced by a time-dependent decay in the SR Ca(2+) content during CICR.
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Affiliation(s)
- Yukiko Himeno
- Biosimulation Research Center, College of Life Sciences, Ritsumeikan University, Shiga, Japan
| | - Keiichi Asakura
- Biosimulation Research Center, College of Life Sciences, Ritsumeikan University, Shiga, Japan; Nippon Shinyaku Co., Ltd., Kyoto, Japan
| | - Chae Young Cha
- Biosimulation Research Center, College of Life Sciences, Ritsumeikan University, Shiga, Japan; Oxford Centre for Diabetes Endocrinology and Metabolism, University of Oxford, Oxford, UK
| | - Hiraku Memida
- Biosimulation Research Center, College of Life Sciences, Ritsumeikan University, Shiga, Japan
| | - Trevor Powell
- Department of Pharmacology, University of Oxford, Oxford, UK
| | - Akira Amano
- Biosimulation Research Center, College of Life Sciences, Ritsumeikan University, Shiga, Japan
| | - Akinori Noma
- Biosimulation Research Center, College of Life Sciences, Ritsumeikan University, Shiga, Japan.
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29
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Wang X, Hardcastle K, Weinberg SH, Smith GD. Population Density and Moment-based Approaches to Modeling Domain Calcium-mediated Inactivation of L-type Calcium Channels. Acta Biotheor 2016; 64:11-32. [PMID: 26424585 DOI: 10.1007/s10441-015-9271-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2015] [Accepted: 09/16/2015] [Indexed: 11/29/2022]
Abstract
We present a population density and moment-based description of the stochastic dynamics of domain [Formula: see text]-mediated inactivation of L-type [Formula: see text] channels. Our approach accounts for the effect of heterogeneity of local [Formula: see text] signals on whole cell [Formula: see text] currents; however, in contrast with prior work, e.g., Sherman et al. (Biophys J 58(4):985-995, 1990), we do not assume that [Formula: see text] domain formation and collapse are fast compared to channel gating. We demonstrate the population density and moment-based modeling approaches using a 12-state Markov chain model of an L-type [Formula: see text] channel introduced by Greenstein and Winslow (Biophys J 83(6):2918-2945, 2002). Simulated whole cell voltage clamp responses yield an inactivation function for the whole cell [Formula: see text] current that agrees with the traditional approach when domain dynamics are fast. We analyze the voltage-dependence of [Formula: see text] inactivation that may occur via slow heterogeneous domain [[Formula: see text]]. Next, we find that when channel permeability is held constant, [Formula: see text]-mediated inactivation of L-type channels increases as the domain time constant increases, because a slow domain collapse rate leads to increased mean domain [[Formula: see text]] near open channels; conversely, when the maximum domain [[Formula: see text]] is held constant, inactivation decreases as the domain time constant increases. Comparison of simulation results using population densities and moment equations confirms the computational efficiency of the moment-based approach, and enables the validation of two distinct methods of truncating and closing the open system of moment equations. In general, a slow domain time constant requires higher order moment truncation for agreement between moment-based and population density simulations.
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Affiliation(s)
- Xiao Wang
- Department of Applied Science, The College of William & Mary, McGlothlin-Street Hall, Rm 305, Williamsburg, VA, 23187, USA
| | - Kiah Hardcastle
- Department of Applied Science, The College of William & Mary, McGlothlin-Street Hall, Rm 305, Williamsburg, VA, 23187, USA
| | - Seth H Weinberg
- Department of Applied Science, The College of William & Mary, McGlothlin-Street Hall, Rm 305, Williamsburg, VA, 23187, USA
| | - Gregory D Smith
- Department of Applied Science, The College of William & Mary, McGlothlin-Street Hall, Rm 305, Williamsburg, VA, 23187, USA.
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30
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Wescott AP, Jafri MS, Lederer WJ, Williams GSB. Ryanodine receptor sensitivity governs the stability and synchrony of local calcium release during cardiac excitation-contraction coupling. J Mol Cell Cardiol 2016; 92:82-92. [PMID: 26827896 PMCID: PMC4807626 DOI: 10.1016/j.yjmcc.2016.01.024] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 10/23/2015] [Revised: 01/13/2016] [Accepted: 01/27/2016] [Indexed: 11/27/2022]
Abstract
Calcium-induced calcium release is the principal mechanism that triggers the cell-wide [Ca(2+)]i transient that activates muscle contraction during cardiac excitation-contraction coupling (ECC). Here, we characterize this process in mouse cardiac myocytes with a novel mathematical action potential (AP) model that incorporates realistic stochastic gating of voltage-dependent L-type calcium (Ca(2+)) channels (LCCs) and sarcoplasmic reticulum (SR) Ca(2+) release channels (the ryanodine receptors, RyR2s). Depolarization of the sarcolemma during an AP stochastically activates the LCCs elevating subspace [Ca(2+)] within each of the cell's 20,000 independent calcium release units (CRUs) to trigger local RyR2 opening and initiate Ca(2+) sparks, the fundamental unit of triggered Ca(2+) release. Synchronization of Ca(2+) sparks during systole depends on the nearly uniform cellular activation of LCCs and the likelihood of local LCC openings triggering local Ca(2+) sparks (ECC fidelity). The detailed design and true SR Ca(2+) pump/leak balance displayed by our model permits investigation of ECC fidelity and Ca(2+) spark fidelity, the balance between visible (Ca(2+) spark) and invisible (Ca(2+) quark/sub-spark) SR Ca(2+) release events. Excess SR Ca(2+) leak is examined as a disease mechanism in the context of "catecholaminergic polymorphic ventricular tachycardia (CPVT)", a Ca(2+)-dependent arrhythmia. We find that that RyR2s (and therefore Ca(2+) sparks) are relatively insensitive to LCC openings across a wide range of membrane potentials; and that key differences exist between Ca(2+) sparks evoked during quiescence, diastole, and systole. The enhanced RyR2 [Ca(2+)]i sensitivity during CPVT leads to increased Ca(2+) spark fidelity resulting in asynchronous systolic Ca(2+) spark activity. It also produces increased diastolic SR Ca(2+) leak with some prolonged Ca(2+) sparks that at times become "metastable" and fail to efficiently terminate. There is a huge margin of safety for stable Ca(2+) handling within the cell and this novel mechanistic model provides insight into the molecular signaling characteristics that help maintain overall Ca(2+) stability even under the conditions of high SR Ca(2+) leak during CPVT. Finally, this model should provide tools for investigators to examine normal and pathological Ca(2+) signaling characteristics in the heart.
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Affiliation(s)
- Andrew P Wescott
- Center for Biomedical Engineering and Technology & Department of Physiology, University of Maryland, Baltimore, Baltimore, MD, United States
| | - M Saleet Jafri
- Center for Biomedical Engineering and Technology & Department of Physiology, University of Maryland, Baltimore, Baltimore, MD, United States; Molecular Neuroscience Department, George Mason University, Fairfax, VA, United States
| | - W J Lederer
- Center for Biomedical Engineering and Technology & Department of Physiology, University of Maryland, Baltimore, Baltimore, MD, United States
| | - George S B Williams
- Center for Biomedical Engineering and Technology & Department of Physiology, University of Maryland, Baltimore, Baltimore, MD, United States.
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Myokit: A simple interface to cardiac cellular electrophysiology. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2015; 120:100-14. [PMID: 26721671 DOI: 10.1016/j.pbiomolbio.2015.12.008] [Citation(s) in RCA: 69] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2015] [Revised: 11/07/2015] [Accepted: 12/16/2015] [Indexed: 11/24/2022]
Abstract
Myokit is a new powerful and versatile software tool for modeling and simulation of cardiac cellular electrophysiology. Myokit consists of an easy-to-read modeling language, a graphical user interface, single and multi-cell simulation engines and a library of advanced analysis tools accessible through a Python interface. Models can be loaded from Myokit's native file format or imported from CellML. Model export is provided to C, MATLAB, CellML, CUDA and OpenCL. Patch-clamp data can be imported and used to estimate model parameters. In this paper, we review existing tools to simulate the cardiac cellular action potential to find that current tools do not cater specifically to model development and that there is a gap between easy-to-use but limited software and powerful tools that require strong programming skills from their users. We then describe Myokit's capabilities, focusing on its model description language, simulation engines and import/export facilities in detail. Using three examples, we show how Myokit can be used for clinically relevant investigations, multi-model testing and parameter estimation in Markov models, all with minimal programming effort from the user. This way, Myokit bridges a gap between performance, versatility and user-friendliness.
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Winslow RL, Walker MA, Greenstein JL. Modeling calcium regulation of contraction, energetics, signaling, and transcription in the cardiac myocyte. WILEY INTERDISCIPLINARY REVIEWS-SYSTEMS BIOLOGY AND MEDICINE 2015; 8:37-67. [PMID: 26562359 DOI: 10.1002/wsbm.1322] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2015] [Revised: 09/29/2015] [Accepted: 09/30/2015] [Indexed: 12/11/2022]
Abstract
Calcium (Ca(2+)) plays many important regulatory roles in cardiac muscle cells. In the initial phase of the action potential, influx of Ca(2+) through sarcolemmal voltage-gated L-type Ca(2+) channels (LCCs) acts as a feed-forward signal that triggers a large release of Ca(2+) from the junctional sarcoplasmic reticulum (SR). This Ca(2+) drives heart muscle contraction and pumping of blood in a process known as excitation-contraction coupling (ECC). Triggered and released Ca(2+) also feed back to inactivate LCCs, attenuating the triggered Ca(2+) signal once release has been achieved. The process of ECC consumes large amounts of ATP. It is now clear that in a process known as excitation-energetics coupling, Ca(2+) signals exert beat-to-beat regulation of mitochondrial ATP production that closely couples energy production with demand. This occurs through transport of Ca(2+) into mitochondria, where it regulates enzymes of the tricarboxylic acid cycle. In excitation-signaling coupling, Ca(2+) activates a number of signaling pathways in a feed-forward manner. Through effects on their target proteins, these interconnected pathways regulate Ca(2+) signals in complex ways to control electrical excitability and contractility of heart muscle. In a process known as excitation-transcription coupling, Ca(2+) acting primarily through signal transduction pathways also regulates the process of gene transcription. Because of these diverse and complex roles, experimentally based mechanistic computational models are proving to be very useful for understanding Ca(2+) signaling in the cardiac myocyte.
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Affiliation(s)
- Raimond L Winslow
- Institute for Computational Medicine and Department of Biomedical Engineering, The Johns Hopkins University School of Medicine and Whiting School of Engineering, Baltimore, MD, USA
| | - Mark A Walker
- Institute for Computational Medicine and Department of Biomedical Engineering, The Johns Hopkins University School of Medicine and Whiting School of Engineering, Baltimore, MD, USA
| | - Joseph L Greenstein
- Institute for Computational Medicine and Department of Biomedical Engineering, The Johns Hopkins University School of Medicine and Whiting School of Engineering, Baltimore, MD, USA
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Ramos-Franco J, Aguilar-Sanchez Y, Escobar AL. Intact Heart Loose Patch Photolysis Reveals Ionic Current Kinetics During Ventricular Action Potentials. Circ Res 2015; 118:203-15. [PMID: 26565013 DOI: 10.1161/circresaha.115.307399] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 08/10/2015] [Accepted: 11/12/2015] [Indexed: 12/16/2022]
Abstract
RATIONALE Assessing the underlying ionic currents during a triggered action potential (AP) in intact perfused hearts offers the opportunity to link molecular mechanisms with pathophysiological problems in cardiovascular research. The developed loose patch photolysis technique can provide striking new insights into cardiac function at the whole heart level during health and disease. OBJECTIVE To measure transmembrane ionic currents during an AP to determine how and when surface Ca(2+) influx that triggers Ca(2+)-induced Ca(2+) release occurs and how Ca(2+)-activated conductances can contribute to the genesis of AP phase 2. METHODS AND RESULTS Loose patch photolysis allows the measurement of transmembrane ionic currents in intact hearts. During a triggered AP, a voltage-dependent Ca(2+) conductance was fractionally activated (dis-inhibited) by rapidly photo-degrading nifedipine, the Ca(2+) channel blocker. The ionic currents during a mouse ventricular AP showed a fast early component and a slower late component. Pharmacological studies established that the molecular basis underlying the early component was driven by an influx of Ca(2+) through the L-type channel, CaV 1.2. The late component was identified as an Na(+)-Ca(2+) exchanger current mediated by Ca(2+) released from the sarcoplasmic reticulum. CONCLUSIONS The novel loose patch photolysis technique allowed the dissection of transmembrane ionic currents in the intact heart. We were able to determine that during an AP, L-type Ca(2+) current contributes to phase 1, whereas Na(+)-Ca(2+) exchanger contributes to phase 2. In addition, loose patch photolysis revealed that the influx of Ca(2+) through L-type Ca(2+) channels terminates because of voltage-dependent deactivation and not by Ca(2+)-dependent inactivation, as commonly believed.
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Affiliation(s)
- Josefina Ramos-Franco
- From the Department of Molecular Biophysics and Physiology, Rush University Medical Center, Chicago, IL (J.R.-F.); and Quantitative Systems Biology Program, School of Natural Sciences (Y.A.-S.) and Biological Engineering and Small Scale Technologies Program, School of Engineering (A.L.E.), University of California, Merced, CA
| | - Yuriana Aguilar-Sanchez
- From the Department of Molecular Biophysics and Physiology, Rush University Medical Center, Chicago, IL (J.R.-F.); and Quantitative Systems Biology Program, School of Natural Sciences (Y.A.-S.) and Biological Engineering and Small Scale Technologies Program, School of Engineering (A.L.E.), University of California, Merced, CA
| | - Ariel L Escobar
- From the Department of Molecular Biophysics and Physiology, Rush University Medical Center, Chicago, IL (J.R.-F.); and Quantitative Systems Biology Program, School of Natural Sciences (Y.A.-S.) and Biological Engineering and Small Scale Technologies Program, School of Engineering (A.L.E.), University of California, Merced, CA.
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34
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Wang X, Weinberg SH, Hao Y, Sobie EA, Smith GD. Calcium homeostasis in a local/global whole cell model of permeabilized ventricular myocytes with a Langevin description of stochastic calcium release. Am J Physiol Heart Circ Physiol 2015; 308:H510-23. [DOI: 10.1152/ajpheart.00296.2014] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
Population density approaches to modeling local control of Ca2+-induced Ca2+ release in cardiac myocytes can be used to construct minimal whole cell models that accurately represent heterogeneous local Ca2+ signals. Unfortunately, the computational complexity of such “local/global” whole cell models scales with the number of Ca2+ release unit (CaRU) states, which is a rapidly increasing function of the number of ryanodine receptors (RyRs) per CaRU. Here we present an alternative approach based on a Langevin description of the collective gating of RyRs coupled by local Ca2+ concentration ([Ca2+]). The computational efficiency of this approach no longer depends on the number of RyRs per CaRU. When the RyR model is minimal, Langevin equations may be replaced by a single Fokker-Planck equation, yielding an extremely compact and efficient local/global whole cell model that reproduces and helps interpret recent experiments that investigate Ca2+ homeostasis in permeabilized ventricular myocytes. Our calculations show that elevated myoplasmic [Ca2+] promotes elevated network sarcoplasmic reticulum (SR) [Ca2+] via SR Ca2+-ATPase-mediated Ca2+ uptake. However, elevated myoplasmic [Ca2+] may also activate RyRs and promote stochastic SR Ca2+ release, which can in turn decrease SR [Ca2+]. Increasing myoplasmic [Ca2+] results in an exponential increase in spark-mediated release and a linear increase in nonspark-mediated release, consistent with recent experiments. The model exhibits two steady-state release fluxes for the same network SR [Ca2+] depending on whether myoplasmic [Ca2+] is low or high. In the later case, spontaneous release decreases SR [Ca2+] in a manner that maintains robust Ca2+ sparks.
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Affiliation(s)
- Xiao Wang
- Department of Applied Science, The College of William and Mary, Williamsburg, Virginia
| | - Seth H. Weinberg
- Department of Applied Science, The College of William and Mary, Williamsburg, Virginia
| | - Yan Hao
- Department of Mathematics and Computer Science, The Hobart and William Smith Colleges, Geneva, New York; and
| | - Eric A. Sobie
- Department of Pharmacology and Systems Therapeutics, Mount Sinai School of Medicine, New York, New York
| | - Gregory D. Smith
- Department of Applied Science, The College of William and Mary, Williamsburg, Virginia
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Weinberg SH. High frequency stimulation of cardiac myocytes: a theoretical and computational study. CHAOS (WOODBURY, N.Y.) 2014; 24:043104. [PMID: 25554024 DOI: 10.1063/1.4897618] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
High-frequency stimulation (HFS) has recently been identified as a novel approach for terminating life-threatening cardiac arrhythmias. HFS elevates myocyte membrane potential and blocks electrical conduction for the duration of the stimulus. However, low amplitude HFS can induce rapidly firing action potentials, which may reinitiate an arrhythmia. The cellular level mechanisms underlying HFS-induced electrical activity are not well understood. Using a multiscale method, we show that a minimal myocyte model qualitatively reproduces the influence of HFS on cardiac electrical activity. Theoretical analysis and simulations suggest that persistent activation and de-inactivation of ionic currents, in particular a fast inward window current, underlie HFS-induced action potentials and membrane potential elevation, providing hypotheses for future experiments. We derive analytical expressions to describe how HFS modifies ionic current amplitude and gating dynamics. We show how fast inward current parameters influence the parameter regimes for HFS-induced electrical activity, demonstrating how the efficacy of HFS as a therapy for terminating arrhythmias may depend on the presence of pathological conditions or pharmacological treatments. Finally, we demonstrate that HFS terminates cardiac arrhythmias in a one-dimensional ring of cardiac tissue. In this study, we demonstrate a novel approach to characterize the influence of HFS on ionic current gating dynamics, provide new insight into HFS of the myocardium, and suggest mechanisms underlying HFS-induced electrical activity.
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Affiliation(s)
- Seth H Weinberg
- Virginia Modeling, Analysis and Simulation Center, Old Dominion University, Suffolk, Virginia 23435, USA
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Abstract
In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.
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Affiliation(s)
- Zhilin Qu
- Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, California 90095, USA
- Correspondence to: Zhilin Qu, PhD, Department of Medicine, Division of Cardiology, David Geffen School of Medicine at UCLA, A2-237 CHS, 650 Charles E. Young Drive South, Los Angeles, CA 90095, Tel: 310-794-6050, Fax: 310-206-9133,
| | - Gang Hu
- Department of Physics, Beijing Normal University, Beijing 100875, China
| | - Alan Garfinkel
- Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, California 90095, USA
- Department of Integrative Biology and Physiology, University of California, Los Angeles, California 90095, USA
| | - James N. Weiss
- Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, California 90095, USA
- Department of Physiology, David Geffen School of Medicine, University of California, Los Angeles, California 90095, USA
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EAD and DAD mechanisms analyzed by developing a new human ventricular cell model. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2014; 116:11-24. [PMID: 25192800 DOI: 10.1016/j.pbiomolbio.2014.08.008] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2014] [Accepted: 08/09/2014] [Indexed: 12/31/2022]
Abstract
It has long been suggested that the Ca(2+)-mechanisms are largely involved in generating the early afterdepolarization (EAD) as well as the delayed afterdepolarization (DAD). This view was examined in a quantitative manner by applying the lead potential analysis to a new human ventricular cell model. In this ventricular cell model, the tight coupled LCC-RyR model (CaRU) based on local control theory (Hinch et al. 2004) and ion channel models mostly based on human electrophysiological data were included to reproduce realistic Ca(2+) dynamics as well as the membrane excitation. Simultaneously, the Ca(2+) accumulation near the Ca(2+) releasing site was incorporated as observed in real cardiac myocytes. The maximum rate of ventricular repolarization (-1.02 mV/ms) is due to IK1 (-0.55 mV/ms) and the rest is provided nearly equally by INCX (-0.20 mV/ms), INaL (-0.16 mV/ms) and INaT (-0.13 mV/ms). These INaL and INaT components are due to closure of the voltage gate, which remains partially open during the plateau potential. DADs could be evoked by applying high-frequency stimulations supplemented by a partial Na(+)/K(+) pump inhibition, or by a microinjection of Ca(2+). EADs was evoked by retarding the inactivation of INaL. The lead potential (VL) analysis revealed that IK1 and IKr played the primary role to reverse the AP repolarization to depolarizing limb of EAD. ICaL and INCX amplified EAD, while the remaining currents partially antagonized dVL/dt. The maximum rate of rise of EAD was attributable to the rapid activation of both ICaL (45.5%) and INCX (54.5%).
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Glynn P, Unudurthi SD, Hund TJ. Mathematical modeling of physiological systems: an essential tool for discovery. Life Sci 2014; 111:1-5. [PMID: 25064823 DOI: 10.1016/j.lfs.2014.07.005] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/27/2014] [Revised: 06/26/2014] [Accepted: 07/02/2014] [Indexed: 10/25/2022]
Abstract
Mathematical models are invaluable tools for understanding the relationships between components of a complex system. In the biological context, mathematical models help us understand the complex web of interrelations between various components (DNA, proteins, enzymes, signaling molecules etc.) in a biological system, gain better understanding of the system as a whole, and in turn predict its behavior in an altered state (e.g. disease). Mathematical modeling has enhanced our understanding of multiple complex biological processes like enzyme kinetics, metabolic networks, signal transduction pathways, gene regulatory networks, and electrophysiology. With recent advances in high throughput data generation methods, computational techniques and mathematical modeling have become even more central to the study of biological systems. In this review, we provide a brief history and highlight some of the important applications of modeling in biological systems with an emphasis on the study of excitable cells. We conclude with a discussion about opportunities and challenges for mathematical modeling going forward. In a larger sense, the review is designed to help answer a simple but important question that theoreticians frequently face from interested but skeptical colleagues on the experimental side: "What is the value of a model?"
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Affiliation(s)
- Patric Glynn
- The Dorothy M. Davis Heart and Lung Research Institute, The Ohio State University Wexner Medical Center, Columbus, OH 43210, USA; Department of Biomedical Engineering, College of Engineering, The Ohio State University, Columbus, OH 43210, USA
| | - Sathya D Unudurthi
- The Dorothy M. Davis Heart and Lung Research Institute, The Ohio State University Wexner Medical Center, Columbus, OH 43210, USA; Department of Biomedical Engineering, College of Engineering, The Ohio State University, Columbus, OH 43210, USA
| | - Thomas J Hund
- The Dorothy M. Davis Heart and Lung Research Institute, The Ohio State University Wexner Medical Center, Columbus, OH 43210, USA; Department of Biomedical Engineering, College of Engineering, The Ohio State University, Columbus, OH 43210, USA; Department of Internal Medicine, The Ohio State University Wexner Medical Center, Columbus, OH 43210, USA.
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Bers DM, Morotti S. Ca(2+) current facilitation is CaMKII-dependent and has arrhythmogenic consequences. Front Pharmacol 2014; 5:144. [PMID: 24987371 PMCID: PMC4060732 DOI: 10.3389/fphar.2014.00144] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2014] [Accepted: 06/02/2014] [Indexed: 11/13/2022] Open
Abstract
The cardiac voltage gated Ca2+ current (ICa) is critical to the electrophysiological properties, excitation-contraction coupling, mitochondrial energetics, and transcriptional regulation in heart. Thus, it is not surprising that cardiac ICa is regulated by numerous pathways. This review will focus on changes in ICa that occur during the cardiac action potential (AP), with particular attention to Ca2+-dependent inactivation (CDI), Ca2+-dependent facilitation (CDF) and how calmodulin (CaM) and Ca2+-CaM dependent protein kinase (CaMKII) participate in the regulation of Ca2+ current during the cardiac AP. CDI depends on CaM pre-bound to the C-terminal of the L-type Ca2+ channel, such that Ca2+ influx and Ca2+ released from the sarcoplasmic reticulum bind to that CaM and cause CDI. In cardiac myocytes CDI normally pre-dominates over voltage-dependent inactivation. The decrease in ICa via CDI provides direct negative feedback on the overall Ca2+ influx during a single beat, when myocyte Ca2+ loading is high. CDF builds up over several beats, depends on CaMKII-dependent Ca2+ channel phosphorylation, and results in a staircase of increasing ICa peak, with progressively slower inactivation. CDF and CDI co-exist and in combination may fine-tune the ICa waveform during the cardiac AP. CDF may partially compensate for the tendency for Ca2+ channel availability to decrease at higher heart rates because of accumulating inactivation. CDF may also allow some reactivation of ICa during long duration cardiac APs, and contribute to early afterdepolarizations, a form of triggered arrhythmias.
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Affiliation(s)
- Donald M Bers
- Department of Pharmacology, University of California Davis Davis, CA, USA
| | - Stefano Morotti
- Department of Pharmacology, University of California Davis Davis, CA, USA
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40
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Greenstein JL, Foteinou PT, Hashambhoy-Ramsay YL, Winslow RL. Modeling CaMKII-mediated regulation of L-type Ca(2+) channels and ryanodine receptors in the heart. Front Pharmacol 2014; 5:60. [PMID: 24772082 PMCID: PMC3982069 DOI: 10.3389/fphar.2014.00060] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2014] [Accepted: 03/18/2014] [Indexed: 11/13/2022] Open
Abstract
Excitation-contraction coupling (ECC) in the cardiac myocyte is mediated by a number of highly integrated mechanisms of intracellular Ca2+ transport. Voltage- and Ca2+-dependent L-type Ca2+ channels (LCCs) allow for Ca2+ entry into the myocyte, which then binds to nearby ryanodine receptors (RyRs) and triggers Ca2+ release from the sarcoplasmic reticulum in a process known as Ca2+-induced Ca2+ release. The highly coordinated Ca2+-mediated interaction between LCCs and RyRs is further regulated by the cardiac isoform of the Ca2+/calmodulin-dependent protein kinase (CaMKII). Because CaMKII targets and modulates the function of many ECC proteins, elucidation of its role in ECC and integrative cellular function is challenging and much insight has been gained through the use of detailed computational models. Multiscale models that can both reconstruct the detailed nature of local signaling events within the cardiac dyad and predict their functional consequences at the level of the whole cell have played an important role in advancing our understanding of CaMKII function in ECC. Here, we review experimentally based models of CaMKII function with a focus on LCC and RyR regulation, and the mechanistic insights that have been gained through their application.
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Affiliation(s)
- Joseph L Greenstein
- Institute for Computational Medicine, Department of Biomedical Engineering, Johns Hopkins University Baltimore, MD, USA
| | - Panagiota T Foteinou
- Institute for Computational Medicine, Department of Biomedical Engineering, Johns Hopkins University Baltimore, MD, USA
| | - Yasmin L Hashambhoy-Ramsay
- Institute for Computational Medicine, Department of Biomedical Engineering, Johns Hopkins University Baltimore, MD, USA
| | - Raimond L Winslow
- Institute for Computational Medicine, Department of Biomedical Engineering, Johns Hopkins University Baltimore, MD, USA
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41
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Wong J, Göktepe S, Kuhl E. Computational modeling of chemo-electro-mechanical coupling: a novel implicit monolithic finite element approach. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2013; 29:1104-33. [PMID: 23798328 PMCID: PMC4567385 DOI: 10.1002/cnm.2565] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2012] [Revised: 02/07/2013] [Accepted: 04/12/2013] [Indexed: 05/05/2023]
Abstract
Computational modeling of the human heart allows us to predict how chemical, electrical, and mechanical fields interact throughout a cardiac cycle. Pharmacological treatment of cardiac disease has advanced significantly over the past decades, yet it remains unclear how the local biochemistry of an individual heart cell translates into global cardiac function. Here, we propose a novel, unified strategy to simulate excitable biological systems across three biological scales. To discretize the governing chemical, electrical, and mechanical equations in space, we propose a monolithic finite element scheme. We apply a highly efficient and inherently modular global-local split, in which the deformation and the transmembrane potential are introduced globally as nodal degrees of freedom, whereas the chemical state variables are treated locally as internal variables. To ensure unconditional algorithmic stability, we apply an implicit backward Euler finite difference scheme to discretize the resulting system in time. To increase algorithmic robustness and guarantee optimal quadratic convergence, we suggest an incremental iterative Newton-Raphson scheme. The proposed algorithm allows us to simulate the interaction of chemical, electrical, and mechanical fields during a representative cardiac cycle on a patient-specific geometry, robust and stable, with calculation times on the order of 4 days on a standard desktop computer.
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Affiliation(s)
- J Wong
- Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, U.S.A
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42
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Ji L, Cheng M, Zhang H. Stochastic contribution for the coding of agonist induced calcium oscillation in hepatocytes. EUROPEAN BIOPHYSICS JOURNAL: EBJ 2013; 42:607-12. [PMID: 23653093 DOI: 10.1007/s00249-013-0908-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2013] [Revised: 04/13/2013] [Accepted: 04/23/2013] [Indexed: 10/26/2022]
Abstract
The influence of stochastic inositol-1,4,5-trisphosphate receptor (IP₃R) dynamics and their clustering have been extensively investigated to explore the mechanism through which the stochastic molecular event finally shape the intracellular calcium signaling. Most of the previous works employed simplified models which take the concentration of IP₃ instead of that of the agonist as the stimulation intensity. However, the IP₃ level is not linearly dependent on the agonist concentration in stimulus induced signaling systems because there are feedback links in the transduction network. In this work, we include both the IP₃R dynamics and the typical agonist induced signaling transduction cascade in the model to investigate the essential influence of stochastic IP₃R dynamics on the coding of the stimulus induced calcium signal. Simulation results reveal two distinct oscillation areas under different stimulation levels. The signal is optimally modulate by the IP₃R cluster number in the weak stimulated area while affected by the stimulus intensity in the strong stimulated area. Different dependences of coefficient of variance (CV) on the number of clusters are obtained in these two areas, which explains the disagreement in the previous reported results. Besides, the transition between these areas explains the significant CV reduction observed in experiments.
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Affiliation(s)
- Lin Ji
- Department of Chemistry, Capital Normal University, Beijing 100048, China.
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43
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Discrete-state stochastic models of calcium-regulated calcium influx and subspace dynamics are not well-approximated by ODEs that neglect concentration fluctuations. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2012; 2012:897371. [PMID: 23509597 PMCID: PMC3594940 DOI: 10.1155/2012/897371] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/29/2012] [Accepted: 09/17/2012] [Indexed: 11/18/2022]
Abstract
Cardiac myocyte calcium signaling is often modeled using deterministic ordinary differential equations (ODEs) and mass-action kinetics. However, spatially restricted "domains" associated with calcium influx are small enough (e.g., 10(-17) liters) that local signaling may involve 1-100 calcium ions. Is it appropriate to model the dynamics of subspace calcium using deterministic ODEs or, alternatively, do we require stochastic descriptions that account for the fundamentally discrete nature of these local calcium signals? To address this question, we constructed a minimal Markov model of a calcium-regulated calcium channel and associated subspace. We compared the expected value of fluctuating subspace calcium concentration (a result that accounts for the small subspace volume) with the corresponding deterministic model (an approximation that assumes large system size). When subspace calcium did not regulate calcium influx, the deterministic and stochastic descriptions agreed. However, when calcium binding altered channel activity in the model, the continuous deterministic description often deviated significantly from the discrete stochastic model, unless the subspace volume is unrealistically large and/or the kinetics of the calcium binding are sufficiently fast. This principle was also demonstrated using a physiologically realistic model of calmodulin regulation of L-type calcium channels introduced by Yue and coworkers.
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44
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Bayer JD, Blake RC, Plank G, Trayanova NA. A novel rule-based algorithm for assigning myocardial fiber orientation to computational heart models. Ann Biomed Eng 2012. [PMID: 22648575 DOI: 10.1007/sl0439-012-0593-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
Electrical waves traveling throughout the myocardium elicit muscle contractions responsible for pumping blood throughout the body. The shape and direction of these waves depend on the spatial arrangement of ventricular myocytes, termed fiber orientation. In computational studies simulating electrical wave propagation or mechanical contraction in the heart, accurately representing fiber orientation is critical so that model predictions corroborate with experimental data. Typically, fiber orientation is assigned to heart models based on Diffusion Tensor Imaging (DTI) data, yet few alternative methodologies exist if DTI data is noisy or absent. Here we present a novel Laplace-Dirichlet Rule-Based (LDRB) algorithm to perform this task with speed, precision, and high usability. We demonstrate the application of the LDRB algorithm in an image-based computational model of the canine ventricles. Simulations of electrical activation in this model are compared to those in the same geometrical model but with DTI-derived fiber orientation. The results demonstrate that activation patterns from simulations with LDRB and DTI-derived fiber orientations are nearly indistinguishable, with relative differences ≤6%, absolute mean differences in activation times ≤3.15 ms, and positive correlations ≥0.99. These results convincingly show that the LDRB algorithm is a robust alternative to DTI for assigning fiber orientation to computational heart models.
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Affiliation(s)
- J D Bayer
- Department of Biomedical Engineering, The Johns Hopkins University, Baltimore, MD, USA.
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45
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Lee YS, Liu OZ, Sobie EA. Decoding myocardial Ca²⁺ signals across multiple spatial scales: a role for sensitivity analysis. J Mol Cell Cardiol 2012; 58:92-9. [PMID: 23026728 DOI: 10.1016/j.yjmcc.2012.09.009] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 08/21/2012] [Accepted: 09/20/2012] [Indexed: 11/28/2022]
Abstract
Numerous studies have employed mathematical modeling to quantitatively understand release of Ca(2+) from the sarcoplasmic reticulum (SR) in the heart. Models have been used to investigate physiologically important phenomena such as triggering of SR Ca(2+) release by Ca(2+) entry across the cell membrane and spontaneous leak of Ca(2+) from the SR in quiescent heart cells. In this review we summarize studies that have modeled myocardial Ca(2+) at different spatial scales: the sub-cellular level, the cellular level, and the multicellular level. We discuss each category of models from the standpoint of parameter sensitivity analysis, a common simulation procedure that can generate quantitative, comprehensive predictions about how changes in conditions influence model output. We propose that this is a useful perspective for conceptualizing models, in part because a sensitivity analysis requires the investigator to define the relevant parameters and model outputs. This procedure therefore helps to illustrate the capabilities and limitations of each model. We further suggest that in future studies, sensitivity analyses will aid in simplifying complex models and in suggesting experiments to differentiate between competing models built with different assumptions. We conclude with a discussion of unresolved questions that are likely to be addressed over the next several years.
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Affiliation(s)
- Young-Seon Lee
- Pharmacology and Systems Therapeutics, Mount Sinai School of Medicine, New York, NY, USA
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46
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Hashambhoy YL, Winslow RL, Greenstein JL. CaMKII-dependent activation of late INa contributes to cellular arrhythmia in a model of the cardiac myocyte. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2012; 2011:4665-8. [PMID: 22255378 DOI: 10.1109/iembs.2011.6091155] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
Cardiac voltage-gated Na(+) channels underlie membrane depolarization during the upstroke of the action potential (AP). These channels also exhibit a late, slowly-inactivating component of current (late I(Na)) that may be enhanced under pathological conditions such as heart failure, and may therefore promote AP prolongation and increase the likelihood of arrhythmia. Ca(2+)/calmodulin-dependent protein kinase II (CaMKII) functionally modifies Na(+) channels, however it remains unclear if the CaMKII-dependent changes in late I(Na) are a major contributor to cellular arrhythmias such as early after depolarizations (EADs). In this study we develop a model of I(Na), including CaMKII-dependent effects, based on experimental measurements. The Na(+) channel model is incorporated into a computational model of the whole myocyte which describes excitation-contraction coupling via stochastic simulation of individual Ca(2+) release sites. Simulations suggest that relatively small augmentation of late I(Na) is sufficient to significantly prolong APs and lead to the appearance of EADs.
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Affiliation(s)
- Yasmin L Hashambhoy
- Department of Biomedical Engineering, Institute for Computational Medicine, TheJohns Hopkins University, Baltimore, MD 21218, USA. du
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47
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Gauthier LD, Greenstein JL, Winslow RL. Toward an integrative computational model of the Guinea pig cardiac myocyte. Front Physiol 2012; 3:244. [PMID: 22783206 PMCID: PMC3389778 DOI: 10.3389/fphys.2012.00244] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2012] [Accepted: 06/14/2012] [Indexed: 11/22/2022] Open
Abstract
The local control theory of excitation-contraction (EC) coupling asserts that regulation of calcium (Ca2+) release occurs at the nanodomain level, where openings of single L-type Ca2+ channels (LCCs) trigger openings of small clusters of ryanodine receptors (RyRs) co-localized within the dyad. A consequence of local control is that the whole-cell Ca2+ transient is a smooth continuous function of influx of Ca2+ through LCCs. While this so-called graded release property has been known for some time, its functional importance to the integrated behavior of the cardiac ventricular myocyte has not been fully appreciated. We previously formulated a biophysically based model, in which LCCs and RyRs interact via a coarse-grained representation of the dyadic space. The model captures key features of local control using a low-dimensional system of ordinary differential equations. Voltage-dependent gain and graded Ca2+ release are emergent properties of this model by virtue of the fact that model formulation is closely based on the sub-cellular basis of local control. In this current work, we have incorporated this graded release model into a prior model of guinea pig ventricular myocyte electrophysiology, metabolism, and isometric force production. The resulting integrative model predicts the experimentally observed causal relationship between action potential (AP) shape and timing of Ca2+ and force transients, a relationship that is not explained by models lacking the graded release property. Model results suggest that even relatively subtle changes in AP morphology that may result, for example, from remodeling of membrane transporter expression in disease or spatial variation in cell properties, may have major impact on the temporal waveform of Ca2+ transients, thus influencing tissue level electromechanical function.
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Affiliation(s)
- Laura Doyle Gauthier
- Department of Biomedical Engineering, Institute for Computational Medicine, The Johns Hopkins University School of Medicine and Whiting School of Engineering Baltimore, MD, USA
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48
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Gaeta SA, Christini DJ. Non-linear dynamics of cardiac alternans: subcellular to tissue-level mechanisms of arrhythmia. Front Physiol 2012; 3:157. [PMID: 22783195 PMCID: PMC3389489 DOI: 10.3389/fphys.2012.00157] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2012] [Accepted: 05/05/2012] [Indexed: 12/22/2022] Open
Abstract
Cardiac repolarization alternans is a rhythm disturbance of the heart in which rapid stimulation elicits a beat-to-beat alternation in the duration of action potentials and magnitude of intracellular calcium transients in individual cardiac myocytes. Although this phenomenon has been identified as a potential precursor to dangerous reentrant arrhythmias and sudden cardiac death, significant uncertainty remains regarding its mechanism and no clinically practical means of halting its occurrence or progression currently exists. Cardiac alternans has well-characterized tissue, cellular, and subcellular manifestations, the mechanisms and interplay of which are an active area of research.
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Affiliation(s)
- Stephen A. Gaeta
- Department of Physiology, Biophysics and Systems
Biology, Weill Cornell Medical CollegeNew York, NY, USA
| | - David J. Christini
- Department of Physiology, Biophysics and Systems
Biology, Weill Cornell Medical CollegeNew York, NY, USA
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49
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Bayer JD, Blake RC, Plank G, Trayanova NA. A novel rule-based algorithm for assigning myocardial fiber orientation to computational heart models. Ann Biomed Eng 2012; 40:2243-54. [PMID: 22648575 DOI: 10.1007/s10439-012-0593-5] [Citation(s) in RCA: 265] [Impact Index Per Article: 22.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2012] [Accepted: 05/10/2012] [Indexed: 12/15/2022]
Abstract
Electrical waves traveling throughout the myocardium elicit muscle contractions responsible for pumping blood throughout the body. The shape and direction of these waves depend on the spatial arrangement of ventricular myocytes, termed fiber orientation. In computational studies simulating electrical wave propagation or mechanical contraction in the heart, accurately representing fiber orientation is critical so that model predictions corroborate with experimental data. Typically, fiber orientation is assigned to heart models based on Diffusion Tensor Imaging (DTI) data, yet few alternative methodologies exist if DTI data is noisy or absent. Here we present a novel Laplace-Dirichlet Rule-Based (LDRB) algorithm to perform this task with speed, precision, and high usability. We demonstrate the application of the LDRB algorithm in an image-based computational model of the canine ventricles. Simulations of electrical activation in this model are compared to those in the same geometrical model but with DTI-derived fiber orientation. The results demonstrate that activation patterns from simulations with LDRB and DTI-derived fiber orientations are nearly indistinguishable, with relative differences ≤6%, absolute mean differences in activation times ≤3.15 ms, and positive correlations ≥0.99. These results convincingly show that the LDRB algorithm is a robust alternative to DTI for assigning fiber orientation to computational heart models.
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Affiliation(s)
- J D Bayer
- Department of Biomedical Engineering, The Johns Hopkins University, Baltimore, MD, USA.
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Nivala M, de Lange E, Rovetti R, Qu Z. Computational modeling and numerical methods for spatiotemporal calcium cycling in ventricular myocytes. Front Physiol 2012; 3:114. [PMID: 22586402 PMCID: PMC3346978 DOI: 10.3389/fphys.2012.00114] [Citation(s) in RCA: 50] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2011] [Accepted: 04/06/2012] [Indexed: 11/13/2022] Open
Abstract
Intracellular calcium (Ca) cycling dynamics in cardiac myocytes is regulated by a complex network of spatially distributed organelles, such as sarcoplasmic reticulum (SR), mitochondria, and myofibrils. In this study, we present a mathematical model of intracellular Ca cycling and numerical and computational methods for computer simulations. The model consists of a coupled Ca release unit (CRU) network, which includes a SR domain and a myoplasm domain. Each CRU contains 10 L-type Ca channels and 100 ryanodine receptor channels, with individual channels simulated stochastically using a variant of Gillespie’s method, modified here to handle time-dependent transition rates. Both the SR domain and the myoplasm domain in each CRU are modeled by 5 × 5 × 5 voxels to maintain proper Ca diffusion. Advanced numerical algorithms implemented on graphical processing units were used for fast computational simulations. For a myocyte containing 100 × 20 × 10 CRUs, a 1-s heart time simulation takes about 10 min of machine time on a single NVIDIA Tesla C2050. Examples of simulated Ca cycling dynamics, such as Ca sparks, Ca waves, and Ca alternans, are shown.
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Affiliation(s)
- Michael Nivala
- Department of Medicine (Cardiology), David Geffen School of Medicine University of California Los Angeles, CA, USA
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